diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index a307d22e456ebf001e6d72beb833555306b21dc6..a6b638c1124094e238d132c6f8decfe1ba1e0742 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -625,6 +625,9 @@ Timeouts
 
             If *when* is a float, it is set as the new deadline.
 
+            if *when* is in the past, the timeout will trigger on the next
+            iteration of the event loop.
+
         .. method:: expired() -> bool
 
            Return whether the context manager has exceeded its deadline
diff --git a/Lib/asyncio/timeouts.py b/Lib/asyncio/timeouts.py
index a89205348ff24ca7043997e83c5870323ed4a86a..94d25535fbc0595760877415166bfc8edd6ba1a8 100644
--- a/Lib/asyncio/timeouts.py
+++ b/Lib/asyncio/timeouts.py
@@ -52,10 +52,10 @@ def reschedule(self, when: Optional[float]) -> None:
             self._timeout_handler = None
         else:
             loop = events.get_running_loop()
-            self._timeout_handler = loop.call_at(
-                when,
-                self._on_timeout,
-            )
+            if when <= loop.time():
+                self._timeout_handler = loop.call_soon(self._on_timeout)
+            else:
+                self._timeout_handler = loop.call_at(when, self._on_timeout)
 
     def expired(self) -> bool:
         """Is timeout expired during execution?"""
diff --git a/Lib/test/test_asyncio/test_timeouts.py b/Lib/test/test_asyncio/test_timeouts.py
index 9801541e55b7f8c02f50b8a3fd3cc1b118c09080..b9bac6f783776b6b8ba324bdeea241233c51de4b 100644
--- a/Lib/test/test_asyncio/test_timeouts.py
+++ b/Lib/test/test_asyncio/test_timeouts.py
@@ -105,6 +105,30 @@ async def test_timeout_zero(self):
         self.assertLess(t1-t0, 2)
         self.assertTrue(t0 <= cm.when() <= t1)
 
+    async def test_timeout_zero_sleep_zero(self):
+        loop = asyncio.get_running_loop()
+        t0 = loop.time()
+        with self.assertRaises(TimeoutError):
+            async with asyncio.timeout(0) as cm:
+                await asyncio.sleep(0)
+        t1 = loop.time()
+        self.assertTrue(cm.expired())
+        # 2 sec for slow CI boxes
+        self.assertLess(t1-t0, 2)
+        self.assertTrue(t0 <= cm.when() <= t1)
+
+    async def test_timeout_in_the_past_sleep_zero(self):
+        loop = asyncio.get_running_loop()
+        t0 = loop.time()
+        with self.assertRaises(TimeoutError):
+            async with asyncio.timeout(-11) as cm:
+                await asyncio.sleep(0)
+        t1 = loop.time()
+        self.assertTrue(cm.expired())
+        # 2 sec for slow CI boxes
+        self.assertLess(t1-t0, 2)
+        self.assertTrue(t0 >= cm.when() <= t1)
+
     async def test_foreign_exception_passed(self):
         with self.assertRaises(KeyError):
             async with asyncio.timeout(0.01) as cm:
diff --git a/Misc/NEWS.d/next/Library/2022-07-21-22-59-22.gh-issue-95109.usxA9r.rst b/Misc/NEWS.d/next/Library/2022-07-21-22-59-22.gh-issue-95109.usxA9r.rst
new file mode 100644
index 0000000000000000000000000000000000000000..40196dd214a283f235f5b041d0bb8aa85baa02a9
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2022-07-21-22-59-22.gh-issue-95109.usxA9r.rst
@@ -0,0 +1 @@
+Ensure that timeouts scheduled with :class:`asyncio.Timeout` that have already expired are delivered promptly.