diff --git a/Lib/multiprocessing/forkserver.py b/Lib/multiprocessing/forkserver.py
index ffd1735848c455..ee5f76780bd0ca 100644
--- a/Lib/multiprocessing/forkserver.py
+++ b/Lib/multiprocessing/forkserver.py
@@ -39,6 +39,25 @@ def __init__(self):
         self._lock = threading.Lock()
         self._preload_modules = ['__main__']
 
+    def _stop(self):
+        # Method used by unit tests to stop the server
+        with self._lock:
+            self._stop_unlocked()
+
+    def _stop_unlocked(self):
+        if self._forkserver_pid is None:
+            return
+
+        # close the "alive" file descriptor asks the server to stop
+        os.close(self._forkserver_alive_fd)
+        self._forkserver_alive_fd = None
+
+        os.waitpid(self._forkserver_pid, 0)
+        self._forkserver_pid = None
+
+        os.unlink(self._forkserver_address)
+        self._forkserver_address = None
+
     def set_forkserver_preload(self, modules_names):
         '''Set list of module names to try to load in forkserver process.'''
         if not all(type(mod) is str for mod in self._preload_modules):
diff --git a/Lib/multiprocessing/util.py b/Lib/multiprocessing/util.py
index f5331abe821fb1..327fe42d6efdb3 100644
--- a/Lib/multiprocessing/util.py
+++ b/Lib/multiprocessing/util.py
@@ -456,3 +456,24 @@ def spawnv_passfds(path, args, passfds):
     finally:
         os.close(errpipe_read)
         os.close(errpipe_write)
+
+
+def _cleanup_tests():
+    """Cleanup multiprocessing resources when multiprocessing tests
+    completed."""
+
+    from test import support
+
+    # cleanup multiprocessing
+    process._cleanup()
+
+    # Stop the ForkServer process if it's running
+    from multiprocessing import forkserver
+    forkserver._forkserver._stop()
+
+    # bpo-37421: Explicitly call _run_finalizers() to remove immediately
+    # temporary directories created by multiprocessing.util.get_temp_dir().
+    _run_finalizers()
+    support.gc_collect()
+
+    support.reap_children()
diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index 30ea23da694991..eb03da9bd4487c 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -5049,8 +5049,8 @@ def tearDownModule():
         # Sleep 500 ms to give time to child processes to complete.
         if need_sleep:
             time.sleep(0.5)
-        multiprocessing.process._cleanup()
-        test.support.gc_collect()
+
+        multiprocessing.util._cleanup_tests()
 
     remote_globs['setUpModule'] = setUpModule
     remote_globs['tearDownModule'] = tearDownModule
diff --git a/Lib/test/test_concurrent_futures.py b/Lib/test/test_concurrent_futures.py
index b42670e16a6c99..a261bfeb4d3734 100644
--- a/Lib/test/test_concurrent_futures.py
+++ b/Lib/test/test_concurrent_futures.py
@@ -26,6 +26,7 @@
     BrokenExecutor)
 from concurrent.futures.process import BrokenProcessPool
 from multiprocessing import get_context
+import multiprocessing.util
 
 
 def create_future(state=PENDING, exception=None, result=None):
@@ -1253,6 +1254,7 @@ def test_main():
         test.support.run_unittest(__name__)
     finally:
         test.support.reap_children()
+        multiprocessing.util._cleanup_tests()
 
 if __name__ == "__main__":
     test_main()
diff --git a/Misc/NEWS.d/next/Tests/2019-07-01-19-57-26.bpo-37421.NFH1f0.rst b/Misc/NEWS.d/next/Tests/2019-07-01-19-57-26.bpo-37421.NFH1f0.rst
new file mode 100644
index 00000000000000..c379b504ba8a41
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-07-01-19-57-26.bpo-37421.NFH1f0.rst
@@ -0,0 +1,2 @@
+multiprocessing tests now explicitly call ``_run_finalizers()`` to
+immediately remove temporary directories created by tests.
diff --git a/Misc/NEWS.d/next/Tests/2019-07-05-14-47-55.bpo-37421.n8o2to.rst b/Misc/NEWS.d/next/Tests/2019-07-05-14-47-55.bpo-37421.n8o2to.rst
new file mode 100644
index 00000000000000..136faa22d47a6e
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-07-05-14-47-55.bpo-37421.n8o2to.rst
@@ -0,0 +1,3 @@
+multiprocessing tests now stop the ForkServer instance if it's running: close
+the "alive" file descriptor to ask the server to stop and then remove its UNIX
+address.