diff --git a/Doc/library/asyncio-eventloop.rst b/Doc/library/asyncio-eventloop.rst
index c51990eff8deec..6fe95687c151de 100644
--- a/Doc/library/asyncio-eventloop.rst
+++ b/Doc/library/asyncio-eventloop.rst
@@ -1271,6 +1271,15 @@ Allows customizing how exceptions are handled in the event loop.
    (see :meth:`call_exception_handler` documentation for details
    about context).
 
+   If the handler is called on behalf of a :class:`~asyncio.Task` or
+   :class:`~asyncio.Handle`, it is run in the
+   :class:`contextvars.Context` of that task or callback handle.
+
+   .. versionchanged:: 3.12
+
+      The handler may be called in the :class:`~contextvars.Context`
+      of the task or handle where the exception originated.
+
 .. method:: loop.get_exception_handler()
 
    Return the current exception handler, or ``None`` if no custom
@@ -1474,6 +1483,13 @@ Callback Handles
    A callback wrapper object returned by :meth:`loop.call_soon`,
    :meth:`loop.call_soon_threadsafe`.
 
+   .. method:: get_context()
+
+      Return the :class:`contextvars.Context` object
+      associated with the handle.
+
+      .. versionadded:: 3.12
+
    .. method:: cancel()
 
       Cancel the callback.  If the callback has already been canceled
diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index ade969220ea701..d922f614954fcd 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -1097,6 +1097,13 @@ Task Object
 
       .. versionadded:: 3.8
 
+   .. method:: get_context()
+
+      Return the :class:`contextvars.Context` object
+      associated with the task.
+
+      .. versionadded:: 3.12
+
    .. method:: get_name()
 
       Return the name of the Task.
diff --git a/Lib/asyncio/base_events.py b/Lib/asyncio/base_events.py
index 66202f09794db8..c8a2f9f25634ef 100644
--- a/Lib/asyncio/base_events.py
+++ b/Lib/asyncio/base_events.py
@@ -1808,7 +1808,22 @@ def call_exception_handler(self, context):
                              exc_info=True)
         else:
             try:
-                self._exception_handler(self, context)
+                ctx = None
+                thing = context.get("task")
+                if thing is None:
+                    # Even though Futures don't have a context,
+                    # Task is a subclass of Future,
+                    # and sometimes the 'future' key holds a Task.
+                    thing = context.get("future")
+                if thing is None:
+                    # Handles also have a context.
+                    thing = context.get("handle")
+                if thing is not None and hasattr(thing, "get_context"):
+                    ctx = thing.get_context()
+                if ctx is not None and hasattr(ctx, "run"):
+                    ctx.run(self._exception_handler, self, context)
+                else:
+                    self._exception_handler(self, context)
             except (SystemExit, KeyboardInterrupt):
                 raise
             except BaseException as exc:
diff --git a/Lib/asyncio/events.py b/Lib/asyncio/events.py
index 0d26ea545baa5d..a327ba54a323a8 100644
--- a/Lib/asyncio/events.py
+++ b/Lib/asyncio/events.py
@@ -61,6 +61,9 @@ def __repr__(self):
         info = self._repr_info()
         return '<{}>'.format(' '.join(info))
 
+    def get_context(self):
+        return self._context
+
     def cancel(self):
         if not self._cancelled:
             self._cancelled = True
diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index e48da0f2008829..8d6dfcd81b7377 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -139,6 +139,9 @@ def __repr__(self):
     def get_coro(self):
         return self._coro
 
+    def get_context(self):
+        return self._context
+
     def get_name(self):
         return self._name
 
diff --git a/Lib/test/test_asyncio/test_futures2.py b/Lib/test/test_asyncio/test_futures2.py
index 71279b69c7929e..9e7a5775a70383 100644
--- a/Lib/test/test_asyncio/test_futures2.py
+++ b/Lib/test/test_asyncio/test_futures2.py
@@ -1,5 +1,6 @@
 # IsolatedAsyncioTestCase based tests
 import asyncio
+import contextvars
 import traceback
 import unittest
 from asyncio import tasks
@@ -27,6 +28,46 @@ async def raise_exc():
             else:
                 self.fail('TypeError was not raised')
 
+    async def test_task_exc_handler_correct_context(self):
+        # see https://github.com/python/cpython/issues/96704
+        name = contextvars.ContextVar('name', default='foo')
+        exc_handler_called = False
+
+        def exc_handler(*args):
+            self.assertEqual(name.get(), 'bar')
+            nonlocal exc_handler_called
+            exc_handler_called = True
+
+        async def task():
+            name.set('bar')
+            1/0
+
+        loop = asyncio.get_running_loop()
+        loop.set_exception_handler(exc_handler)
+        self.cls(task())
+        await asyncio.sleep(0)
+        self.assertTrue(exc_handler_called)
+
+    async def test_handle_exc_handler_correct_context(self):
+        # see https://github.com/python/cpython/issues/96704
+        name = contextvars.ContextVar('name', default='foo')
+        exc_handler_called = False
+
+        def exc_handler(*args):
+            self.assertEqual(name.get(), 'bar')
+            nonlocal exc_handler_called
+            exc_handler_called = True
+
+        def callback():
+            name.set('bar')
+            1/0
+
+        loop = asyncio.get_running_loop()
+        loop.set_exception_handler(exc_handler)
+        loop.call_soon(callback)
+        await asyncio.sleep(0)
+        self.assertTrue(exc_handler_called)
+
 @unittest.skipUnless(hasattr(tasks, '_CTask'),
                        'requires the C _asyncio module')
 class CFutureTests(FutureTests, unittest.IsolatedAsyncioTestCase):
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 04bdf648313148..2491285206bcd7 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -2482,6 +2482,17 @@ def test_get_coro(self):
         finally:
             loop.close()
 
+    def test_get_context(self):
+        loop = asyncio.new_event_loop()
+        coro = coroutine_function()
+        context = contextvars.copy_context()
+        try:
+            task = self.new_task(loop, coro, context=context)
+            loop.run_until_complete(task)
+            self.assertIs(task.get_context(), context)
+        finally:
+            loop.close()
+
 
 def add_subclass_tests(cls):
     BaseTask = cls.Task
diff --git a/Misc/NEWS.d/next/Library/2022-09-18-04-51-30.gh-issue-96704.DmamRX.rst b/Misc/NEWS.d/next/Library/2022-09-18-04-51-30.gh-issue-96704.DmamRX.rst
new file mode 100644
index 00000000000000..6ac99197e685c1
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2022-09-18-04-51-30.gh-issue-96704.DmamRX.rst
@@ -0,0 +1 @@
+Pass the correct ``contextvars.Context`` when a ``asyncio`` exception handler is called on behalf of a task or callback handle. This adds a new ``Task`` method, ``get_context``, and also a new ``Handle`` method with the same name. If this method is not found on a task object (perhaps because it is a third-party library that does not yet provide this method), the context prevailing at the time the exception handler is called is used.
diff --git a/Modules/_asynciomodule.c b/Modules/_asynciomodule.c
index 909171150bdd36..efa0d2d6906eab 100644
--- a/Modules/_asynciomodule.c
+++ b/Modules/_asynciomodule.c
@@ -2409,6 +2409,18 @@ _asyncio_Task_get_coro_impl(TaskObj *self)
     return self->task_coro;
 }
 
+/*[clinic input]
+_asyncio.Task.get_context
+[clinic start generated code]*/
+
+static PyObject *
+_asyncio_Task_get_context_impl(TaskObj *self)
+/*[clinic end generated code: output=6996f53d3dc01aef input=87c0b209b8fceeeb]*/
+{
+    Py_INCREF(self->task_context);
+    return self->task_context;
+}
+
 /*[clinic input]
 _asyncio.Task.get_name
 [clinic start generated code]*/
@@ -2536,6 +2548,7 @@ static PyMethodDef TaskType_methods[] = {
     _ASYNCIO_TASK_GET_NAME_METHODDEF
     _ASYNCIO_TASK_SET_NAME_METHODDEF
     _ASYNCIO_TASK_GET_CORO_METHODDEF
+    _ASYNCIO_TASK_GET_CONTEXT_METHODDEF
     {"__class_getitem__", Py_GenericAlias, METH_O|METH_CLASS, PyDoc_STR("See PEP 585")},
     {NULL, NULL}        /* Sentinel */
 };
diff --git a/Modules/clinic/_asynciomodule.c.h b/Modules/clinic/_asynciomodule.c.h
index daf524c3456ca8..ddec54c8d7c2bc 100644
--- a/Modules/clinic/_asynciomodule.c.h
+++ b/Modules/clinic/_asynciomodule.c.h
@@ -772,6 +772,23 @@ _asyncio_Task_get_coro(TaskObj *self, PyObject *Py_UNUSED(ignored))
     return _asyncio_Task_get_coro_impl(self);
 }
 
+PyDoc_STRVAR(_asyncio_Task_get_context__doc__,
+"get_context($self, /)\n"
+"--\n"
+"\n");
+
+#define _ASYNCIO_TASK_GET_CONTEXT_METHODDEF    \
+    {"get_context", (PyCFunction)_asyncio_Task_get_context, METH_NOARGS, _asyncio_Task_get_context__doc__},
+
+static PyObject *
+_asyncio_Task_get_context_impl(TaskObj *self);
+
+static PyObject *
+_asyncio_Task_get_context(TaskObj *self, PyObject *Py_UNUSED(ignored))
+{
+    return _asyncio_Task_get_context_impl(self);
+}
+
 PyDoc_STRVAR(_asyncio_Task_get_name__doc__,
 "get_name($self, /)\n"
 "--\n"
@@ -1172,4 +1189,4 @@ _asyncio__leave_task(PyObject *module, PyObject *const *args, Py_ssize_t nargs,
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=459a7c7f21bbc290 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=f117b2246eaf7a55 input=a9049054013a1b77]*/