diff --git a/CHANGES/7188.feature b/CHANGES/7188.feature
new file mode 100644
index 00000000000..777144aa0e2
--- /dev/null
+++ b/CHANGES/7188.feature
@@ -0,0 +1 @@
+Added a graceful shutdown period which allows pending tasks to complete before the application's cleanup is called. The period can be adjusted with the ``shutdown_timeout`` parameter -- by :user:`Dreamsorcerer`.
diff --git a/aiohttp/test_utils.py b/aiohttp/test_utils.py
index e0aacbb68fc..652a8d4713d 100644
--- a/aiohttp/test_utils.py
+++ b/aiohttp/test_utils.py
@@ -115,7 +115,7 @@ async def start_server(self, **kwargs: Any) -> None:
         if self.runner:
             return
         self._ssl = kwargs.pop("ssl", None)
-        self.runner = await self._make_runner(**kwargs)
+        self.runner = await self._make_runner(handler_cancellation=True, **kwargs)
         await self.runner.setup()
         if not self.port:
             self.port = 0
diff --git a/aiohttp/web_fileresponse.py b/aiohttp/web_fileresponse.py
index cdb0fe58923..ce85eeb6a69 100644
--- a/aiohttp/web_fileresponse.py
+++ b/aiohttp/web_fileresponse.py
@@ -283,4 +283,4 @@ async def prepare(self, request: "BaseRequest") -> Optional[AbstractStreamWriter
         try:
             return await self._sendfile(request, fobj, offset, count)
         finally:
-            await loop.run_in_executor(None, fobj.close)
+            await asyncio.shield(loop.run_in_executor(None, fobj.close))
diff --git a/aiohttp/web_runner.py b/aiohttp/web_runner.py
index 4b1408c31a6..8dad92bab0e 100644
--- a/aiohttp/web_runner.py
+++ b/aiohttp/web_runner.py
@@ -2,6 +2,7 @@
 import signal
 import socket
 from abc import ABC, abstractmethod
+from contextlib import suppress
 from typing import Any, List, Optional, Set, Type
 
 from yarl import URL
@@ -80,11 +81,26 @@ async def stop(self) -> None:
         # named pipes do not have wait_closed property
         if hasattr(self._server, "wait_closed"):
             await self._server.wait_closed()
+
+        # Wait for pending tasks for a given time limit.
+        with suppress(asyncio.TimeoutError):
+            await asyncio.wait_for(
+                self._wait(asyncio.current_task()), timeout=self._shutdown_timeout
+            )
+
         await self._runner.shutdown()
         assert self._runner.server
         await self._runner.server.shutdown(self._shutdown_timeout)
         self._runner._unreg_site(self)
 
+    async def _wait(self, parent_task: Optional["asyncio.Task[object]"]) -> None:
+        exclude = self._runner.starting_tasks | {asyncio.current_task(), parent_task}
+        # TODO(PY38): while tasks := asyncio.all_tasks() - exclude:
+        tasks = asyncio.all_tasks() - exclude
+        while tasks:
+            await asyncio.wait(tasks)
+            tasks = asyncio.all_tasks() - exclude
+
 
 class TCPSite(BaseSite):
     __slots__ = ("_host", "_port", "_reuse_address", "_reuse_port")
@@ -247,7 +263,7 @@ async def start(self) -> None:
 
 
 class BaseRunner(ABC):
-    __slots__ = ("_handle_signals", "_kwargs", "_server", "_sites")
+    __slots__ = ("starting_tasks", "_handle_signals", "_kwargs", "_server", "_sites")
 
     def __init__(self, *, handle_signals: bool = False, **kwargs: Any) -> None:
         self._handle_signals = handle_signals
@@ -287,6 +303,11 @@ async def setup(self) -> None:
                 pass
 
         self._server = await self._make_server()
+        # On shutdown we want to avoid waiting on tasks which run forever.
+        # It's very likely that all tasks which run forever will have been created by
+        # the time we have completed the application startup (in self._make_server()),
+        # so we just record all running tasks here and exclude them later.
+        self.starting_tasks = asyncio.all_tasks()
 
     @abstractmethod
     async def shutdown(self) -> None:
diff --git a/docs/web_advanced.rst b/docs/web_advanced.rst
index bf71d11fce0..6055ddaf319 100644
--- a/docs/web_advanced.rst
+++ b/docs/web_advanced.rst
@@ -927,8 +927,14 @@ Graceful shutdown
 Stopping *aiohttp web server* by just closing all connections is not
 always satisfactory.
 
-The problem is: if application supports :term:`websocket`\s or *data
-streaming* it most likely has open connections at server
+The first thing aiohttp will do is to stop listening on the sockets,
+so new connections will be rejected. It will then wait a few
+seconds to allow any pending tasks to complete before continuing
+with application shutdown. The timeout can be adjusted with
+``shutdown_timeout`` in :func:`run_app`.
+
+Another problem is if the application supports :term:`websockets <websocket>` or
+*data streaming* it most likely has open connections at server
 shutdown time.
 
 The *library* has no knowledge how to close them gracefully but
diff --git a/docs/web_reference.rst b/docs/web_reference.rst
index f37c3da854b..05210f17199 100644
--- a/docs/web_reference.rst
+++ b/docs/web_reference.rst
@@ -2688,9 +2688,10 @@ application on specific TCP or Unix socket, e.g.::
 
    :param int port: PORT to listed on, ``8080`` if ``None`` (default).
 
-   :param float shutdown_timeout: a timeout for closing opened
-                                  connections on :meth:`BaseSite.stop`
-                                  call.
+   :param float shutdown_timeout: a timeout used for both waiting on pending
+                                  tasks before application shutdown and for
+                                  closing opened connections on
+                                  :meth:`BaseSite.stop` call.
 
    :param ssl_context: a :class:`ssl.SSLContext` instance for serving
                        SSL/TLS secure server, ``None`` for plain HTTP
@@ -2723,9 +2724,10 @@ application on specific TCP or Unix socket, e.g.::
 
    :param str path: PATH to UNIX socket to listen.
 
-   :param float shutdown_timeout: a timeout for closing opened
-                                  connections on :meth:`BaseSite.stop`
-                                  call.
+   :param float shutdown_timeout: a timeout used for both waiting on pending
+                                  tasks before application shutdown and for
+                                  closing opened connections on
+                                  :meth:`BaseSite.stop` call.
 
    :param ssl_context: a :class:`ssl.SSLContext` instance for serving
                        SSL/TLS secure server, ``None`` for plain HTTP
@@ -2745,9 +2747,10 @@ application on specific TCP or Unix socket, e.g.::
 
    :param str path: PATH of named pipe to listen.
 
-   :param float shutdown_timeout: a timeout for closing opened
-                                  connections on :meth:`BaseSite.stop`
-                                  call.
+   :param float shutdown_timeout: a timeout used for both waiting on pending
+                                  tasks before application shutdown and for
+                                  closing opened connections on
+                                  :meth:`BaseSite.stop` call.
 
 .. class:: SockSite(runner, sock, *, \
                    shutdown_timeout=60.0, ssl_context=None, \
@@ -2759,9 +2762,10 @@ application on specific TCP or Unix socket, e.g.::
 
    :param sock: A :ref:`socket instance <socket-objects>` to listen to.
 
-   :param float shutdown_timeout: a timeout for closing opened
-                                  connections on :meth:`BaseSite.stop`
-                                  call.
+   :param float shutdown_timeout: a timeout used for both waiting on pending
+                                  tasks before application shutdown and for
+                                  closing opened connections on
+                                  :meth:`BaseSite.stop` call.
 
    :param ssl_context: a :class:`ssl.SSLContext` instance for serving
                        SSL/TLS secure server, ``None`` for plain HTTP
@@ -2857,9 +2861,13 @@ Utilities
                                 shutdown before disconnecting all
                                 open client sockets hard way.
 
+                                This is used as a delay to wait for
+                                pending tasks to complete and then
+                                again to close any pending connections.
+
                                 A system with properly
                                 :ref:`aiohttp-web-graceful-shutdown`
-                                implemented never waits for this
+                                implemented never waits for the second
                                 timeout but closes a server in a few
                                 milliseconds.
 
diff --git a/tests/test_run_app.py b/tests/test_run_app.py
index 46b868c3815..d7ab4b9de4b 100644
--- a/tests/test_run_app.py
+++ b/tests/test_run_app.py
@@ -9,14 +9,15 @@
 import ssl
 import subprocess
 import sys
-from typing import Any
+import time
+from typing import Any, Callable, NoReturn
 from unittest import mock
 from uuid import uuid4
 
 import pytest
 from conftest import needs_unix
 
-from aiohttp import web
+from aiohttp import ClientConnectorError, ClientSession, web
 from aiohttp.test_utils import make_mocked_coro
 from aiohttp.web_runner import BaseRunner
 
@@ -926,3 +927,197 @@ async def init():
 
     web.run_app(init(), print=stopper(patched_loop), loop=patched_loop)
     assert count == 3
+
+
+class TestShutdown:
+    def raiser(self) -> NoReturn:
+        raise KeyboardInterrupt
+
+    async def stop(self, request: web.Request) -> web.Response:
+        asyncio.get_running_loop().call_soon(self.raiser)
+        return web.Response()
+
+    def run_app(self, port: int, timeout: int, task, extra_test=None) -> asyncio.Task:
+        async def test() -> None:
+            await asyncio.sleep(1)
+            async with ClientSession() as sess:
+                async with sess.get(f"http://localhost:{port}/"):
+                    pass
+                async with sess.get(f"http://localhost:{port}/stop"):
+                    pass
+
+                if extra_test:
+                    await extra_test(sess)
+
+        async def run_test(app: web.Application) -> None:
+            nonlocal test_task
+            test_task = asyncio.create_task(test())
+            yield
+            await test_task
+
+        async def handler(request: web.Request) -> web.Response:
+            nonlocal t
+            t = asyncio.create_task(task())
+            return web.Response(text="FOO")
+
+        t = test_task = None
+        app = web.Application()
+        app.cleanup_ctx.append(run_test)
+        app.router.add_get("/", handler)
+        app.router.add_get("/stop", self.stop)
+
+        web.run_app(app, port=port, shutdown_timeout=timeout)
+        assert test_task.exception() is None
+        return t
+
+    def test_shutdown_wait_for_task(
+        self, aiohttp_unused_port: Callable[[], int]
+    ) -> None:
+        port = aiohttp_unused_port()
+        finished = False
+
+        async def task():
+            nonlocal finished
+            await asyncio.sleep(2)
+            finished = True
+
+        t = self.run_app(port, 3, task)
+
+        assert finished is True
+        assert t.done()
+        assert not t.cancelled()
+
+    def test_shutdown_timeout_task(
+        self, aiohttp_unused_port: Callable[[], int]
+    ) -> None:
+        port = aiohttp_unused_port()
+        finished = False
+
+        async def task():
+            nonlocal finished
+            await asyncio.sleep(2)
+            finished = True
+
+        t = self.run_app(port, 1, task)
+
+        assert finished is False
+        assert t.done()
+        assert t.cancelled()
+
+    def test_shutdown_wait_for_spawned_task(
+        self, aiohttp_unused_port: Callable[[], int]
+    ) -> None:
+        port = aiohttp_unused_port()
+        finished = False
+        finished_sub = False
+        sub_t = None
+
+        async def sub_task():
+            nonlocal finished_sub
+            await asyncio.sleep(1.5)
+            finished_sub = True
+
+        async def task():
+            nonlocal finished, sub_t
+            await asyncio.sleep(0.5)
+            sub_t = asyncio.create_task(sub_task())
+            finished = True
+
+        t = self.run_app(port, 3, task)
+
+        assert finished is True
+        assert t.done()
+        assert not t.cancelled()
+        assert finished_sub is True
+        assert sub_t.done()
+        assert not sub_t.cancelled()
+
+    def test_shutdown_timeout_not_reached(
+        self, aiohttp_unused_port: Callable[[], int]
+    ) -> None:
+        port = aiohttp_unused_port()
+        finished = False
+
+        async def task():
+            nonlocal finished
+            await asyncio.sleep(1)
+            finished = True
+
+        start_time = time.time()
+        t = self.run_app(port, 15, task)
+
+        assert finished is True
+        assert t.done()
+        # Verify run_app has not waited for timeout.
+        assert time.time() - start_time < 10
+
+    def test_shutdown_new_conn_rejected(
+        self, aiohttp_unused_port: Callable[[], int]
+    ) -> None:
+        port = aiohttp_unused_port()
+        finished = False
+
+        async def task() -> None:
+            nonlocal finished
+            await asyncio.sleep(9)
+            finished = True
+
+        async def test(sess: ClientSession) -> None:
+            # Ensure we are in the middle of shutdown (waiting for task()).
+            await asyncio.sleep(1)
+            with pytest.raises(ClientConnectorError):
+                # Use a new session to try and open a new connection.
+                async with ClientSession() as sess:
+                    async with sess.get(f"http://localhost:{port}/"):
+                        pass
+            assert finished is False
+
+        t = self.run_app(port, 10, task, test)
+
+        assert finished is True
+        assert t.done()
+
+    def test_shutdown_pending_handler_responds(
+        self, aiohttp_unused_port: Callable[[], int]
+    ) -> None:
+        port = aiohttp_unused_port()
+        finished = False
+
+        async def test() -> None:
+            async def test_resp(sess):
+                async with sess.get(f"http://localhost:{port}/") as resp:
+                    assert await resp.text() == "FOO"
+
+            await asyncio.sleep(1)
+            async with ClientSession() as sess:
+                t = asyncio.create_task(test_resp(sess))
+                await asyncio.sleep(1)
+                # Handler is in-progress while we trigger server shutdown.
+                async with sess.get(f"http://localhost:{port}/stop"):
+                    pass
+
+                assert finished is False
+                # Handler should still complete and produce a response.
+                await t
+
+        async def run_test(app: web.Application) -> None:
+            nonlocal t
+            t = asyncio.create_task(test())
+            yield
+            await t
+
+        async def handler(request: web.Request) -> web.Response:
+            nonlocal finished
+            await asyncio.sleep(3)
+            finished = True
+            return web.Response(text="FOO")
+
+        t = None
+        app = web.Application()
+        app.cleanup_ctx.append(run_test)
+        app.router.add_get("/", handler)
+        app.router.add_get("/stop", self.stop)
+
+        web.run_app(app, port=port, shutdown_timeout=5)
+        assert t.exception() is None
+        assert finished is True