diff --git a/distributed/process.py b/distributed/process.py
index debbf025cc6..0663229ccc5 100644
--- a/distributed/process.py
+++ b/distributed/process.py
@@ -1,13 +1,16 @@
 from __future__ import annotations
 
 import asyncio
+import inspect
 import logging
 import multiprocessing
 import os
 import re
 import threading
 import weakref
+from collections.abc import Callable
 from queue import Queue as PyQueue
+from typing import TypeVar
 
 from tornado.concurrent import Future
 from tornado.ioloop import IOLoop
@@ -47,6 +50,9 @@ class _ProcessState:
     exitcode = None
 
 
+_T_async_process = TypeVar("_T_async_process", bound="AsyncProcess")
+
+
 class AsyncProcess:
     """
     A coroutine-compatible multiprocessing.Process-alike.
@@ -126,9 +132,9 @@ def stop_thread(q):
         self._thread_finalizer = weakref.finalize(self, stop_thread, q=self._watch_q)
         self._thread_finalizer.atexit = False
 
-    def _on_exit(self, exitcode):
+    def _on_exit(self, exitcode: int) -> None:
         # Called from the event loop when the child process exited
-        self._process = None
+        self._process = None  # type: ignore[assignment]
         if self._exit_callback is not None:
             self._exit_callback(self)
         self._exit_future.set_result(exitcode)
@@ -311,14 +317,19 @@ def close(self):
             self._process = None
             self._closed = True
 
-    def set_exit_callback(self, func):
+    def set_exit_callback(
+        self: _T_async_process, func: Callable[[_T_async_process], None]
+    ) -> None:
         """
         Set a function to be called by the event loop when the process exits.
         The function is called with the AsyncProcess as sole argument.
 
-        The function may be a coroutine function.
+        The function may not be a coroutine function.
         """
         # XXX should this be a property instead?
+        assert not inspect.iscoroutinefunction(
+            func
+        ), "exit callback may not be a coroutine function"
         assert callable(func), "exit callback should be callable"
         assert (
             self._state.pid is None