diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index 596cb7565a66e7d..f0ad36096dd8570 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -843,17 +843,16 @@ Timeouts
    Wait for the *fut* :ref:`awaitable <asyncio-awaitables>`
    to complete with a timeout.
 
-   If *fut* is a coroutine it is automatically scheduled as a Task.
+   If *fut* is a coroutine, it is awaited directly rather than being wrapped
+   in a :class:`Task`, unless *timeout* is zero or negative.
 
    *timeout* can either be ``None`` or a float or int number of seconds
    to wait for.  If *timeout* is ``None``, block until the future
    completes.
 
-   If a timeout occurs, it cancels the task and raises
-   :exc:`TimeoutError`.
+   If a timeout occurs, it cancels *fut* and raises :exc:`TimeoutError`.
 
-   To avoid the task :meth:`cancellation <Task.cancel>`,
-   wrap it in :func:`shield`.
+   To prevent *fut* from being cancelled, wrap it in :func:`shield`.
 
    The function will wait until the future is actually cancelled,
    so the total wait time may exceed the *timeout*. If an exception
@@ -894,6 +893,10 @@ Timeouts
    .. versionchanged:: 3.11
       Raises :exc:`TimeoutError` instead of :exc:`asyncio.TimeoutError`.
 
+   .. versionchanged:: 3.12
+      Implemented using :func:`asyncio.timeout`, a coroutine passed as *fut*
+      is no longer wrapped in a :class:`Task` when *timeout* is positive.
+
 
 Waiting primitives
 ==================
diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 7889d4793a5dec3..129bcf7c838a096 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -440,15 +440,16 @@ def _release_waiter(waiter, *args):
 async def wait_for(fut, timeout):
     """Wait for the single Future or coroutine to complete, with timeout.
 
-    Coroutine will be wrapped in Task.
+    A coroutine is awaited directly rather than being wrapped in a Task,
+    unless timeout is zero or negative.
 
     Returns result of the Future or coroutine.  When a timeout occurs,
-    it cancels the task and raises TimeoutError.  To avoid the task
-    cancellation, wrap it in shield().
+    it cancels fut and raises TimeoutError.  To prevent fut from being
+    cancelled, wrap it in shield().
 
-    If the wait is cancelled, the task is also cancelled.
+    If the wait is cancelled, fut is also cancelled.
 
-    If the task suppresses the cancellation and returns a value instead,
+    If fut suppresses the cancellation and returns a value instead,
     that value is returned.
 
     This function is a coroutine.