diff --git a/CHANGES/6807.bugfix.rst b/CHANGES/6807.bugfix.rst
new file mode 100644
index 00000000000..4eb07b9e0da
--- /dev/null
+++ b/CHANGES/6807.bugfix.rst
@@ -0,0 +1 @@
+Stopped logging exceptions from ``web.run_app()`` that would be raised regardless -- by :user:`Dreamsorcerer`.
diff --git a/aiohttp/web.py b/aiohttp/web.py
index b56560d733e..650fe3417d0 100644
--- a/aiohttp/web.py
+++ b/aiohttp/web.py
@@ -6,6 +6,7 @@
 import warnings
 from argparse import ArgumentParser
 from collections.abc import Iterable
+from contextlib import suppress
 from importlib import import_module
 from typing import (
     Any,
@@ -501,11 +502,15 @@ def run_app(
     except (GracefulExit, KeyboardInterrupt):  # pragma: no cover
         pass
     finally:
-        _cancel_tasks({main_task}, loop)
-        _cancel_tasks(asyncio.all_tasks(loop), loop)
-        loop.run_until_complete(loop.shutdown_asyncgens())
-        loop.close()
-        asyncio.set_event_loop(None)
+        try:
+            main_task.cancel()
+            with suppress(asyncio.CancelledError):
+                loop.run_until_complete(main_task)
+        finally:
+            _cancel_tasks(asyncio.all_tasks(loop), loop)
+            loop.run_until_complete(loop.shutdown_asyncgens())
+            loop.close()
+            asyncio.set_event_loop(None)
 
 
 def main(argv: List[str]) -> None:
diff --git a/tests/test_run_app.py b/tests/test_run_app.py
index 4a94099f2d5..3fa8dc11303 100644
--- a/tests/test_run_app.py
+++ b/tests/test_run_app.py
@@ -979,6 +979,23 @@ async def init() -> web.Application:
     assert count == 3
 
 
+def test_run_app_raises_exception(patched_loop: asyncio.AbstractEventLoop) -> None:
+    async def context(app: web.Application) -> AsyncIterator[None]:
+        raise RuntimeError("foo")
+        yield  # pragma: no cover
+
+    app = web.Application()
+    app.cleanup_ctx.append(context)
+
+    with mock.patch.object(
+        patched_loop, "call_exception_handler", autospec=True, spec_set=True
+    ) as m:
+        with pytest.raises(RuntimeError, match="foo"):
+            web.run_app(app, loop=patched_loop)
+
+    assert not m.called
+
+
 class TestShutdown:
     def raiser(self) -> NoReturn:
         raise KeyboardInterrupt