diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index c37f0e1387980c..7ecec9638489df 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -445,8 +445,13 @@ async def wait_for(fut, timeout, *, loop=None):
         if fut.done():
             return fut.result()
 
-        fut.cancel()
-        raise exceptions.TimeoutError()
+        await _cancel_and_wait(fut, loop=loop)
+        try:
+            fut.result()
+        except exceptions.CancelledError as exc:
+            raise exceptions.TimeoutError() from exc
+        else:
+            raise exceptions.TimeoutError()
 
     waiter = loop.create_future()
     timeout_handle = loop.call_later(timeout, _release_waiter, waiter)
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index f9db066ce89837..511961c32005a0 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -1131,6 +1131,9 @@ async def inner():
                 nonlocal task_done
                 try:
                     await asyncio.sleep(0.2)
+                except asyncio.CancelledError:
+                    await asyncio.sleep(_EPSILON)
+                    raise
                 finally:
                     task_done = True
 
@@ -1145,6 +1148,34 @@ async def inner():
         chained = cm.exception.__context__
         self.assertEqual(type(chained), asyncio.CancelledError)
 
+    def test_wait_for_waits_for_task_cancellation_w_timeout_0(self):
+        loop = asyncio.new_event_loop()
+        self.addCleanup(loop.close)
+
+        task_done = False
+
+        async def foo():
+            async def inner():
+                nonlocal task_done
+                try:
+                    await asyncio.sleep(10)
+                except asyncio.CancelledError:
+                    await asyncio.sleep(_EPSILON)
+                    raise
+                finally:
+                    task_done = True
+
+            inner_task = self.new_task(loop, inner())
+            await asyncio.sleep(_EPSILON)
+            await asyncio.wait_for(inner_task, timeout=0)
+
+        with self.assertRaises(asyncio.TimeoutError) as cm:
+            loop.run_until_complete(foo())
+
+        self.assertTrue(task_done)
+        chained = cm.exception.__context__
+        self.assertEqual(type(chained), asyncio.CancelledError)
+
     def test_wait_for_reraises_exception_during_cancellation(self):
         loop = asyncio.new_event_loop()
         self.addCleanup(loop.close)
diff --git a/Misc/NEWS.d/next/Library/2020-08-15-15-50-12.bpo-32751.85je5X.rst b/Misc/NEWS.d/next/Library/2020-08-15-15-50-12.bpo-32751.85je5X.rst
new file mode 100644
index 00000000000000..c172ce5d9e9487
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-08-15-15-50-12.bpo-32751.85je5X.rst
@@ -0,0 +1,3 @@
+When cancelling the task due to a timeout, :meth:`asyncio.wait_for` will now
+wait until the cancellation is complete also in the case when *timeout* is
+<= 0, like it does with positive timeouts.