diff --git a/doc/api/stream.md b/doc/api/stream.md
index ac9ea0afd8f331..082679ce80728d 100644
--- a/doc/api/stream.md
+++ b/doc/api/stream.md
@@ -2798,11 +2798,16 @@ const server = http.createServer((req, res) => {
 
 <!-- YAML
 added: v16.9.0
+changes:
+  - version: REPLACEME
+    pr-url: https://github.com/nodejs/node/pull/46675
+    description: Added support for webstreams.
 -->
 
 > Stability: 1 - `stream.compose` is experimental.
 
-* `streams` {Stream\[]|Iterable\[]|AsyncIterable\[]|Function\[]}
+* `streams` {Stream\[]|Iterable\[]|AsyncIterable\[]|Function\[]|
+  ReadableStream\[]|WritableStream\[]|TransformStream\[]}
 * Returns: {stream.Duplex}
 
 Combines two or more streams into a `Duplex` stream that writes to the
diff --git a/lib/internal/streams/compose.js b/lib/internal/streams/compose.js
index 03bfa39e9f6f1b..06d6883ce62fc3 100644
--- a/lib/internal/streams/compose.js
+++ b/lib/internal/streams/compose.js
@@ -7,6 +7,10 @@ const {
   isNodeStream,
   isReadable,
   isWritable,
+  isWebStream,
+  isTransformStream,
+  isWritableStream,
+  isReadableStream,
 } = require('internal/streams/utils');
 const {
   AbortError,
@@ -15,6 +19,7 @@ const {
     ERR_MISSING_ARGS,
   },
 } = require('internal/errors');
+const eos = require('internal/streams/end-of-stream');
 
 module.exports = function compose(...streams) {
   if (streams.length === 0) {
@@ -37,18 +42,32 @@ module.exports = function compose(...streams) {
   }
 
   for (let n = 0; n < streams.length; ++n) {
-    if (!isNodeStream(streams[n])) {
+    if (!isNodeStream(streams[n]) && !isWebStream(streams[n])) {
       // TODO(ronag): Add checks for non streams.
       continue;
     }
-    if (n < streams.length - 1 && !isReadable(streams[n])) {
+    if (
+      n < streams.length - 1 &&
+      !(
+        isReadable(streams[n]) ||
+        isReadableStream(streams[n]) ||
+        isTransformStream(streams[n])
+      )
+    ) {
       throw new ERR_INVALID_ARG_VALUE(
         `streams[${n}]`,
         orgStreams[n],
         'must be readable'
       );
     }
-    if (n > 0 && !isWritable(streams[n])) {
+    if (
+      n > 0 &&
+      !(
+        isWritable(streams[n]) ||
+        isWritableStream(streams[n]) ||
+        isTransformStream(streams[n])
+      )
+    ) {
       throw new ERR_INVALID_ARG_VALUE(
         `streams[${n}]`,
         orgStreams[n],
@@ -79,8 +98,16 @@ module.exports = function compose(...streams) {
   const head = streams[0];
   const tail = pipeline(streams, onfinished);
 
-  const writable = !!isWritable(head);
-  const readable = !!isReadable(tail);
+  const writable = !!(
+    isWritable(head) ||
+    isWritableStream(head) ||
+    isTransformStream(head)
+  );
+  const readable = !!(
+    isReadable(tail) ||
+    isReadableStream(tail) ||
+    isTransformStream(tail)
+  );
 
   // TODO(ronag): Avoid double buffering.
   // Implement Writable/Readable/Duplex traits.
@@ -94,28 +121,55 @@ module.exports = function compose(...streams) {
   });
 
   if (writable) {
-    d._write = function(chunk, encoding, callback) {
-      if (head.write(chunk, encoding)) {
-        callback();
-      } else {
-        ondrain = callback;
-      }
-    };
-
-    d._final = function(callback) {
-      head.end();
-      onfinish = callback;
-    };
+    if (isNodeStream(head)) {
+      d._write = function(chunk, encoding, callback) {
+        if (head.write(chunk, encoding)) {
+          callback();
+        } else {
+          ondrain = callback;
+        }
+      };
+
+      d._final = function(callback) {
+        head.end();
+        onfinish = callback;
+      };
+
+      head.on('drain', function() {
+        if (ondrain) {
+          const cb = ondrain;
+          ondrain = null;
+          cb();
+        }
+      });
+    } else if (isWebStream(head)) {
+      const writable = isTransformStream(head) ? head.writable : head;
+      const writer = writable.getWriter();
+
+      d._write = async function(chunk, encoding, callback) {
+        try {
+          await writer.ready;
+          writer.write(chunk).catch(() => {});
+          callback();
+        } catch (err) {
+          callback(err);
+        }
+      };
+
+      d._final = async function(callback) {
+        try {
+          await writer.ready;
+          writer.close().catch(() => {});
+          onfinish = callback;
+        } catch (err) {
+          callback(err);
+        }
+      };
+    }
 
-    head.on('drain', function() {
-      if (ondrain) {
-        const cb = ondrain;
-        ondrain = null;
-        cb();
-      }
-    });
+    const toRead = isTransformStream(tail) ? tail.readable : tail;
 
-    tail.on('finish', function() {
+    eos(toRead, () => {
       if (onfinish) {
         const cb = onfinish;
         onfinish = null;
@@ -125,32 +179,54 @@ module.exports = function compose(...streams) {
   }
 
   if (readable) {
-    tail.on('readable', function() {
-      if (onreadable) {
-        const cb = onreadable;
-        onreadable = null;
-        cb();
-      }
-    });
-
-    tail.on('end', function() {
-      d.push(null);
-    });
-
-    d._read = function() {
-      while (true) {
-        const buf = tail.read();
-
-        if (buf === null) {
-          onreadable = d._read;
-          return;
+    if (isNodeStream(tail)) {
+      tail.on('readable', function() {
+        if (onreadable) {
+          const cb = onreadable;
+          onreadable = null;
+          cb();
         }
-
-        if (!d.push(buf)) {
-          return;
+      });
+
+      tail.on('end', function() {
+        d.push(null);
+      });
+
+      d._read = function() {
+        while (true) {
+          const buf = tail.read();
+          if (buf === null) {
+            onreadable = d._read;
+            return;
+          }
+
+          if (!d.push(buf)) {
+            return;
+          }
         }
-      }
-    };
+      };
+    } else if (isWebStream(tail)) {
+      const readable = isTransformStream(tail) ? tail.readable : tail;
+      const reader = readable.getReader();
+      d._read = async function() {
+        while (true) {
+          try {
+            const { value, done } = await reader.read();
+
+            if (!d.push(value)) {
+              return;
+            }
+
+            if (done) {
+              d.push(null);
+              return;
+            }
+          } catch {
+            return;
+          }
+        }
+      };
+    }
   }
 
   d._destroy = function(err, callback) {
@@ -166,7 +242,9 @@ module.exports = function compose(...streams) {
       callback(err);
     } else {
       onclose = callback;
-      destroyer(tail, err);
+      if (isNodeStream(tail)) {
+        destroyer(tail, err);
+      }
     }
   };
 
diff --git a/lib/internal/streams/pipeline.js b/lib/internal/streams/pipeline.js
index 44c0e06ee30557..4a78e1c4698874 100644
--- a/lib/internal/streams/pipeline.js
+++ b/lib/internal/streams/pipeline.js
@@ -285,7 +285,7 @@ function pipelineImpl(streams, callback, opts) {
           throw new ERR_INVALID_RETURN_VALUE(
             'Iterable, AsyncIterable or Stream', 'source', ret);
         }
-      } else if (isIterable(stream) || isReadableNodeStream(stream)) {
+      } else if (isIterable(stream) || isReadableNodeStream(stream) || isTransformStream(stream)) {
         ret = stream;
       } else {
         ret = Duplex.from(stream);
@@ -384,6 +384,7 @@ function pipelineImpl(streams, callback, opts) {
         finishCount++;
         pumpToWeb(ret, stream, finish, { end });
       } else if (isTransformStream(ret)) {
+        finishCount++;
         pumpToWeb(ret.readable, stream, finish, { end });
       } else {
         throw new ERR_INVALID_ARG_TYPE(
diff --git a/test/parallel/test-webstreams-compose.js b/test/parallel/test-webstreams-compose.js
new file mode 100644
index 00000000000000..5514d12bd02eb0
--- /dev/null
+++ b/test/parallel/test-webstreams-compose.js
@@ -0,0 +1,483 @@
+'use strict';
+
+const common = require('../common');
+const assert = require('assert');
+
+const {
+  Transform,
+  Readable,
+  Writable,
+  compose
+} = require('stream');
+
+const {
+  TransformStream,
+  ReadableStream,
+  WritableStream,
+} = require('stream/web');
+
+{
+  let res = '';
+
+  const d = compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk?.toString()?.replace(' ', '_'));
+      })
+    }),
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk?.toString()?.toUpperCase());
+      })
+    })
+  );
+
+  d.on('data', common.mustCall((chunk) => {
+    res += chunk;
+  }));
+
+  d.on('end', common.mustCall(() => {
+    assert.strictEqual(res, 'HELLO_WORLD');
+  }));
+
+  d.end('hello world');
+}
+
+{
+  let res = '';
+
+  compose(
+    new Transform({
+      transform: common.mustCall((chunk, encoding, callback) => {
+        callback(null, chunk + chunk);
+      })
+    }),
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      })
+    })
+  )
+  .end('asd')
+  .on('data', common.mustCall((buf) => {
+    res += buf;
+  }))
+  .on('end', common.mustCall(() => {
+    assert.strictEqual(res, 'ASDASD');
+  }));
+}
+
+{
+  let res = '';
+
+  compose(
+    async function*(source) {
+      for await (const chunk of source) {
+        yield chunk + chunk;
+      }
+    },
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      }),
+    })
+  )
+  .end('asd')
+  .on('data', common.mustCall((buf) => {
+    res += buf;
+  }))
+  .on('end', common.mustCall(() => {
+    assert.strictEqual(res, 'ASDASD');
+  }));
+}
+
+{
+  let res = '';
+
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      }),
+    }),
+    async function*(source) {
+      for await (const chunk of source) {
+        yield chunk + chunk;
+      }
+    },
+    new Transform({
+      transform: common.mustCall((chunk, enc, clb) => {
+        clb(null, chunk?.toString()?.replaceAll('A', 'B'));
+      })
+    })
+  )
+  .end('asd')
+  .on('data', common.mustCall((buf) => {
+    res += buf;
+  }))
+  .on('end', common.mustCall(() => {
+    assert.strictEqual(res, 'BSDBSD');
+  }));
+}
+
+{
+  let res = '';
+
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      }),
+    }),
+    async function*(source) {
+      for await (const chunk of source) {
+        yield chunk + chunk;
+      }
+    },
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk?.toString()?.replaceAll('A', 'B'));
+      })
+    })
+  )
+  .end('asd')
+  .on('data', common.mustCall((buf) => {
+    res += buf;
+  }))
+  .on('end', common.mustCall(() => {
+    assert.strictEqual(res, 'BSDBSD');
+  }));
+}
+
+{
+  let res = '';
+  compose(
+    new ReadableStream({
+      start(controller) {
+        controller.enqueue('asd');
+        controller.close();
+      }
+    }),
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk?.toString()?.toUpperCase());
+      })
+    })
+  )
+  .on('data', common.mustCall((buf) => {
+    res += buf;
+  }))
+  .on('end', common.mustCall(() => {
+    assert.strictEqual(res, 'ASD');
+  }));
+}
+
+{
+  let res = '';
+  compose(
+    new ReadableStream({
+      start(controller) {
+        controller.enqueue('asd');
+        controller.close();
+      }
+    }),
+    new Transform({
+      transform: common.mustCall((chunk, enc, clb) => {
+        clb(null, chunk?.toString()?.toUpperCase());
+      })
+    })
+  )
+  .on('data', common.mustCall((buf) => {
+    res += buf;
+  }))
+  .on('end', common.mustCall(() => {
+    assert.strictEqual(res, 'ASD');
+  }));
+}
+
+{
+  let res = '';
+  compose(
+    Readable.from(['asd']),
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk?.toString()?.toUpperCase());
+      })
+    })
+  )
+  .on('data', common.mustCall((buf) => {
+    res += buf;
+  }))
+  .on('end', common.mustCall(() => {
+    assert.strictEqual(res, 'ASD');
+  }));
+}
+
+{
+  let res = '';
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      })
+    }),
+    async function*(source) {
+      for await (const chunk of source) {
+        yield chunk;
+      }
+    },
+    new Writable({
+      write: common.mustCall((chunk, encoding, callback) => {
+        res += chunk;
+        callback(null);
+      })
+    })
+  )
+    .end('asd')
+    .on('finish', common.mustCall(() => {
+      assert.strictEqual(res, 'ASD');
+    }));
+}
+
+{
+  let res = '';
+  compose(
+    new Transform({
+      transform: common.mustCall((chunk, encoding, callback) => {
+        callback(null, chunk.toString().toUpperCase());
+      })
+    }),
+    async function*(source) {
+      for await (const chunk of source) {
+        yield chunk;
+      }
+    },
+    new WritableStream({
+      write: common.mustCall((chunk) => {
+        res += chunk;
+      })
+    })
+  )
+  .end('asd')
+  .on('finish', common.mustCall(() => {
+    assert.strictEqual(res, 'ASD');
+  }));
+}
+
+{
+  let res = '';
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      })
+    }),
+    async function*(source) {
+      for await (const chunk of source) {
+        yield chunk;
+      }
+    },
+    new WritableStream({
+      write: common.mustCall((chunk) => {
+        res += chunk;
+      })
+    })
+  )
+  .end('asd')
+  .on('finish', common.mustCall(() => {
+    assert.strictEqual(res, 'ASD');
+  }));
+}
+
+{
+  let res = '';
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      })
+    }),
+    async function*(source) {
+      for await (const chunk of source) {
+        yield chunk;
+      }
+    },
+    async function(source) {
+      for await (const chunk of source) {
+        res += chunk;
+      }
+    }
+  )
+  .end('asd')
+  .on('finish', common.mustCall(() => {
+    assert.strictEqual(res, 'ASD');
+  }));
+}
+
+{
+
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.error(new Error('asd'));
+      })
+    }),
+    new TransformStream({
+      transform: common.mustNotCall()
+    })
+  )
+  .on('data', common.mustNotCall())
+  .on('end', common.mustNotCall())
+  .on('error', (err) => {
+    assert.strictEqual(err?.message, 'asd');
+  })
+  .end('xyz');
+}
+
+{
+
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk);
+      })
+    }),
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.error(new Error('asd'));
+      })
+    })
+  )
+  .on('data', common.mustNotCall())
+  .on('end', common.mustNotCall())
+  .on('error', (err) => {
+    assert.strictEqual(err?.message, 'asd');
+  })
+  .end('xyz');
+}
+
+{
+
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk);
+      })
+    }),
+    async function*(source) { // eslint-disable-line require-yield
+      let tmp = '';
+      for await (const chunk of source) {
+        tmp += chunk;
+        throw new Error('asd');
+      }
+      return tmp;
+    },
+    new TransformStream({
+      transform: common.mustNotCall()
+    })
+  )
+  .on('data', common.mustNotCall())
+  .on('end', common.mustNotCall())
+  .on('error', (err) => {
+    assert.strictEqual(err?.message, 'asd');
+  })
+  .end('xyz');
+}
+
+{
+
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.error(new Error('asd'));
+      })
+    }),
+    new Transform({
+      transform: common.mustNotCall()
+    })
+  )
+  .on('data', common.mustNotCall())
+  .on('end', common.mustNotCall())
+  .on('error', (err) => {
+    assert.strictEqual(err?.message, 'asd');
+  })
+  .end('xyz');
+}
+
+{
+
+  compose(
+    new Transform({
+      transform: common.mustCall((chunk, enc, clb) => {
+        clb(new Error('asd'));
+      })
+    }),
+    new TransformStream({
+      transform: common.mustNotCall()
+    })
+  )
+  .on('data', common.mustNotCall())
+  .on('end', common.mustNotCall())
+  .on('error', (err) => {
+    assert.strictEqual(err?.message, 'asd');
+  })
+  .end('xyz');
+}
+
+{
+  compose(
+    new ReadableStream({
+      start(controller) {
+        controller.enqueue(new Error('asd'));
+      }
+    }),
+    new TransformStream({
+      transform: common.mustNotCall()
+    })
+  )
+  .on('data', common.mustNotCall())
+  .on('end', common.mustNotCall())
+  .on('error', (err) => {
+    assert.strictEqual(err?.message, 'asd');
+  })
+  .end('xyz');
+}
+
+{
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      })
+    }),
+    new WritableStream({
+      write: common.mustCall((chunk, controller) => {
+        controller.error(new Error('asd'));
+      })
+    })
+  )
+  .on('error', (err) => {
+    assert.strictEqual(err?.message, 'asd');
+  })
+  .end('xyz');
+}
+
+{
+  compose(
+    new TransformStream({
+      transform: common.mustCall((chunk, controller) => {
+        controller.enqueue(chunk.toString().toUpperCase());
+      })
+    }),
+    async function*(source) {
+      for await (const chunk of source) {
+        yield chunk;
+      }
+    },
+    async function(source) {
+      throw new Error('asd');
+    }
+  ).on('error', (err) => {
+    assert.strictEqual(err?.message, 'asd');
+  }).end('xyz');
+}