diff --git a/django/test/runner.py b/django/test/runner.py
index eb5026b212..225bc19b09 100644
--- a/django/test/runner.py
+++ b/django/test/runner.py
@@ -561,7 +561,7 @@ class DiscoverRunner:
                  reverse=False, debug_mode=False, debug_sql=False, parallel=0,
                  tags=None, exclude_tags=None, test_name_patterns=None,
                  pdb=False, buffer=False, enable_faulthandler=True,
-                 timing=False, shuffle=False, **kwargs):
+                 timing=False, shuffle=False, logger=None, **kwargs):
 
         self.pattern = pattern
         self.top_level = top_level
@@ -595,6 +595,7 @@ class DiscoverRunner:
             }
         self.shuffle = shuffle
         self._shuffler = None
+        self.logger = logger
 
     @classmethod
     def add_arguments(cls, parser):
@@ -677,16 +678,23 @@ class DiscoverRunner:
 
     def log(self, msg, level=None):
         """
-        Log the given message at the given logging level.
+        Log the message at the given logging level (the default is INFO).
 
-        A verbosity of 1 logs INFO (the default level) or above, and verbosity
-        2 or higher logs all levels.
+        If a logger isn't set, the message is instead printed to the console,
+        respecting the configured verbosity. A verbosity of 0 prints no output,
+        a verbosity of 1 prints INFO and above, and a verbosity of 2 or higher
+        prints all levels.
         """
-        if self.verbosity <= 0 or (
-            self.verbosity == 1 and level is not None and level < logging.INFO
-        ):
-            return
-        print(msg)
+        if level is None:
+            level = logging.INFO
+        if self.logger is None:
+            if self.verbosity <= 0 or (
+                self.verbosity == 1 and level < logging.INFO
+            ):
+                return
+            print(msg)
+        else:
+            self.logger.log(level, msg)
 
     def setup_test_environment(self, **kwargs):
         setup_test_environment(debug=self.debug_mode)
diff --git a/docs/releases/4.0.txt b/docs/releases/4.0.txt
index 24ce7285e0..aa45d1e1e9 100644
--- a/docs/releases/4.0.txt
+++ b/docs/releases/4.0.txt
@@ -356,8 +356,11 @@ Tests
 * Django test runner now supports a :option:`--buffer <test --buffer>` option
   with parallel tests.
 
-* The new :meth:`.DiscoverRunner.log` method allows customizing the way
-  messages are logged.
+* The new ``logger`` argument to :class:`~django.test.runner.DiscoverRunner`
+  allows a Python :py:ref:`logger <logger>` to be used for logging.
+
+* The new :meth:`.DiscoverRunner.log` method provides a way to log messages
+  that uses the ``DiscoverRunner.logger``, or prints to the console if not set.
 
 * Django test runner now supports a :option:`--shuffle <test --shuffle>` option
   to execute tests in a random order.
diff --git a/docs/topics/testing/advanced.txt b/docs/topics/testing/advanced.txt
index 3265c5c641..c0251d8368 100644
--- a/docs/topics/testing/advanced.txt
+++ b/docs/topics/testing/advanced.txt
@@ -510,7 +510,7 @@ behavior. This class defines the ``run_tests()`` entry point, plus a
 selection of other methods that are used by ``run_tests()`` to set up, execute
 and tear down the test suite.
 
-.. class:: DiscoverRunner(pattern='test*.py', top_level=None, verbosity=1, interactive=True, failfast=False, keepdb=False, reverse=False, debug_mode=False, debug_sql=False, parallel=0, tags=None, exclude_tags=None, test_name_patterns=None, pdb=False, buffer=False, enable_faulthandler=True, timing=True, shuffle=False, **kwargs)
+.. class:: DiscoverRunner(pattern='test*.py', top_level=None, verbosity=1, interactive=True, failfast=False, keepdb=False, reverse=False, debug_mode=False, debug_sql=False, parallel=0, tags=None, exclude_tags=None, test_name_patterns=None, pdb=False, buffer=False, enable_faulthandler=True, timing=True, shuffle=False, logger=None, **kwargs)
 
     ``DiscoverRunner`` will search for tests in any file matching ``pattern``.
 
@@ -580,10 +580,15 @@ and tear down the test suite.
     If ``shuffle`` is an integer, test cases will be shuffled in a random order
     prior to execution, using the integer as a random seed. If ``shuffle`` is
     ``None``, the seed will be generated randomly. In both cases, the seed will
-    be logged to the console and set to ``self.shuffle_seed`` prior to running
-    tests. This option can be used to help detect tests that aren't properly
-    isolated. :ref:`Grouping by test class <order-of-tests>` is preserved when
-    using this option.
+    be logged and set to ``self.shuffle_seed`` prior to running tests. This
+    option can be used to help detect tests that aren't properly isolated.
+    :ref:`Grouping by test class <order-of-tests>` is preserved when using this
+    option.
+
+    ``logger`` can be used to pass a Python :py:ref:`Logger object <logger>`.
+    If provided, the logger will be used to log messages instead of printing to
+    the console. The logger object will respect its logging level rather than
+    the ``verbosity``.
 
     Django may, from time to time, extend the capabilities of the test runner
     by adding new arguments. The ``**kwargs`` declaration allows for this
@@ -601,7 +606,7 @@ and tear down the test suite.
 
     .. versionadded:: 4.0
 
-        The ``shuffle`` argument was added.
+        The ``logger`` and ``shuffle`` arguments were added.
 
 Attributes
 ~~~~~~~~~~
@@ -726,11 +731,13 @@ Methods
 
     .. versionadded:: 4.0
 
-    Prints to the console a message with the given integer `logging level`_
-    (e.g. ``logging.DEBUG``, ``logging.INFO``, or ``logging.WARNING``),
-    respecting the current ``verbosity``. For example, an ``INFO`` message will
-    be logged if the ``verbosity`` is at least 1, and ``DEBUG`` will be logged
-    if it is at least 2.
+    If a ``logger`` is set, logs the message at the given integer
+    `logging level`_ (e.g. ``logging.DEBUG``, ``logging.INFO``, or
+    ``logging.WARNING``). Otherwise, the message is printed to the console,
+    respecting the current ``verbosity``. For example, no message will be
+    printed if the ``verbosity`` is 0, ``INFO`` and above will be printed if
+    the ``verbosity`` is at least 1, and ``DEBUG`` will be printed if it is at
+    least 2. The ``level`` defaults to ``logging.INFO``.
 
 .. _`logging level`: https://docs.python.org/3/library/logging.html#levels
 
diff --git a/tests/test_runner/test_discover_runner.py b/tests/test_runner/test_discover_runner.py
index 625de94067..0012be5a7e 100644
--- a/tests/test_runner/test_discover_runner.py
+++ b/tests/test_runner/test_discover_runner.py
@@ -623,6 +623,27 @@ class DiscoverRunnerTests(SimpleTestCase):
                     runner.log(msg, level)
                     self.assertEqual(stdout.getvalue(), f'{msg}\n' if output else '')
 
+    def test_log_logger(self):
+        logger = logging.getLogger('test.logging')
+        cases = [
+            (None, 'INFO:test.logging:log message'),
+            # Test a low custom logging level.
+            (5, 'Level 5:test.logging:log message'),
+            (logging.DEBUG, 'DEBUG:test.logging:log message'),
+            (logging.INFO, 'INFO:test.logging:log message'),
+            (logging.WARNING, 'WARNING:test.logging:log message'),
+            # Test a high custom logging level.
+            (45, 'Level 45:test.logging:log message'),
+        ]
+        for level, expected in cases:
+            with self.subTest(level=level):
+                runner = DiscoverRunner(logger=logger)
+                # Pass a logging level smaller than the smallest level in cases
+                # in order to capture all messages.
+                with self.assertLogs('test.logging', level=1) as cm:
+                    runner.log('log message', level)
+                self.assertEqual(cm.output, [expected])
+
 
 class DiscoverRunnerGetDatabasesTests(SimpleTestCase):
     runner = DiscoverRunner(verbosity=2)