diff --git a/django/utils/dateformat.py b/django/utils/dateformat.py
index afd36d79e0..c4d9d035e4 100644
--- a/django/utils/dateformat.py
+++ b/django/utils/dateformat.py
@@ -325,8 +325,8 @@ class DateFormat(TimeFormat):
         return self.data.isocalendar()[1]
 
     def y(self):
-        "Year, 2 digits; e.g. '99'"
-        return str(self.data.year)[2:]
+        """Year, 2 digits with leading zeros; e.g. '99'."""
+        return '%02d' % (self.data.year % 100)
 
     def Y(self):
         "Year, 4 digits; e.g. '1999'"
diff --git a/docs/ref/templates/builtins.txt b/docs/ref/templates/builtins.txt
index 1c79f3a2f5..17528cea18 100644
--- a/docs/ref/templates/builtins.txt
+++ b/docs/ref/templates/builtins.txt
@@ -1379,7 +1379,7 @@ Format character  Description                               Example output
                   style. Proprietary extension.
 ``t``             Number of days in the given month.        ``28`` to ``31``
 **Year**
-``y``             Year, 2 digits.                           ``'99'``
+``y``             Year, 2 digits with leading zeros.        ``'00'`` to ``'99'``
 ``Y``             Year, 4 digits.                           ``'1999'``
 ``L``             Boolean for whether it's a leap year.     ``True`` or ``False``
 ``o``             ISO-8601 week-numbering year,             ``'1999'``
diff --git a/tests/utils_tests/test_dateformat.py b/tests/utils_tests/test_dateformat.py
index d050ac4352..5eb166e2bd 100644
--- a/tests/utils_tests/test_dateformat.py
+++ b/tests/utils_tests/test_dateformat.py
@@ -165,3 +165,16 @@ class DateFormatTests(SimpleTestCase):
                 dateformat.format(dt, 'r'),
                 'Sun, 08 Jul 1979 22:00:00 +0100',
             )
+
+    def test_year_before_1000(self):
+        tests = [
+            (476, '76'),
+            (42, '42'),
+            (4, '04'),
+        ]
+        for year, expected_date in tests:
+            with self.subTest(year=year):
+                self.assertEqual(
+                    dateformat.format(datetime(year, 9, 8, 5, 0), 'y'),
+                    expected_date,
+                )