diff --git a/doc/users/next_whats_new/gif_savefig.rst b/doc/users/next_whats_new/gif_savefig.rst
new file mode 100644
index 000000000000..e6f4732e8b95
--- /dev/null
+++ b/doc/users/next_whats_new/gif_savefig.rst
@@ -0,0 +1,6 @@
+Saving figures as GIF works again
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+According to the figure documentation, the ``savefig`` method supports the
+GIF format with the file extension ``.gif``. However, GIF support had been
+broken since Matplotlib 2.0.0. It works again.
diff --git a/galleries/examples/lines_bars_and_markers/fill_between_alpha.py b/galleries/examples/lines_bars_and_markers/fill_between_alpha.py
index f462f6bf2428..487ae9aaf62d 100644
--- a/galleries/examples/lines_bars_and_markers/fill_between_alpha.py
+++ b/galleries/examples/lines_bars_and_markers/fill_between_alpha.py
@@ -44,7 +44,7 @@
 # regions can overlap and alpha allows you to see both.  Note that the
 # postscript format does not support alpha (this is a postscript
 # limitation, not a matplotlib limitation), so when using alpha save
-# your figures in PNG, PDF or SVG.
+# your figures in GIF, PNG, PDF or SVG.
 #
 # Our next example computes two populations of random walkers with a
 # different mean and standard deviation of the normal distributions from
diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index cd39db6c3a51..4d087911a5b2 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -62,6 +62,7 @@
 _log = logging.getLogger(__name__)
 _default_filetypes = {
     'eps': 'Encapsulated Postscript',
+    'gif': 'Graphics Interchange Format',
     'jpg': 'Joint Photographic Experts Group',
     'jpeg': 'Joint Photographic Experts Group',
     'pdf': 'Portable Document Format',
@@ -78,6 +79,7 @@
 }
 _default_backends = {
     'eps': 'matplotlib.backends.backend_ps',
+    'gif': 'matplotlib.backends.backend_agg',
     'jpg': 'matplotlib.backends.backend_agg',
     'jpeg': 'matplotlib.backends.backend_agg',
     'pdf': 'matplotlib.backends.backend_pdf',
diff --git a/lib/matplotlib/backends/backend_agg.py b/lib/matplotlib/backends/backend_agg.py
index c37427369267..b435ae565ce4 100644
--- a/lib/matplotlib/backends/backend_agg.py
+++ b/lib/matplotlib/backends/backend_agg.py
@@ -490,6 +490,9 @@ def print_to_buffer(self):
     # print_figure(), and the latter ensures that `self.figure.dpi` already
     # matches the dpi kwarg (if any).
 
+    def print_gif(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
+        self._print_pil(filename_or_obj, "gif", pil_kwargs, metadata)
+
     def print_jpg(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
         # savefig() has already applied savefig.facecolor; we now set it to
         # white to make imsave() blend semi-transparent figures against an
@@ -507,7 +510,7 @@ def print_tif(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
     def print_webp(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
         self._print_pil(filename_or_obj, "webp", pil_kwargs, metadata)
 
-    print_jpg.__doc__, print_tif.__doc__, print_webp.__doc__ = map(
+    print_gif.__doc__, print_jpg.__doc__, print_tif.__doc__, print_webp.__doc__ = map(
         """
         Write the figure to a {} file.
 
@@ -518,7 +521,7 @@ def print_webp(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
         pil_kwargs : dict, optional
             Additional keyword arguments that are passed to
             `PIL.Image.Image.save` when saving the figure.
-        """.format, ["JPEG", "TIFF", "WebP"])
+        """.format, ["GIF", "JPEG", "TIFF", "WebP"])
 
 
 @_Backend.export
diff --git a/lib/matplotlib/testing/compare.py b/lib/matplotlib/testing/compare.py
index 0f252bc1da8e..c598dfcddc66 100644
--- a/lib/matplotlib/testing/compare.py
+++ b/lib/matplotlib/testing/compare.py
@@ -99,6 +99,16 @@ def _read_until(self, terminator):
                 return bytes(buf)
 
 
+class _MagickConverter:
+    def __call__(self, orig, dest):
+        try:
+            subprocess.run(
+                [mpl._get_executable_info("magick").executable, orig, dest],
+                check=True)
+        except subprocess.CalledProcessError as e:
+            raise _ConverterError() from e
+
+
 class _GSConverter(_Converter):
     def __call__(self, orig, dest):
         if not self._proc:
@@ -230,6 +240,12 @@ def __call__(self, orig, dest):
 
 
 def _update_converter():
+    try:
+        mpl._get_executable_info("magick")
+    except mpl.ExecutableNotFoundError:
+        pass
+    else:
+        converter['gif'] = _MagickConverter()
     try:
         mpl._get_executable_info("gs")
     except mpl.ExecutableNotFoundError:
diff --git a/lib/matplotlib/testing/decorators.py b/lib/matplotlib/testing/decorators.py
index 6f1af7debdb3..af9ef48d66cc 100644
--- a/lib/matplotlib/testing/decorators.py
+++ b/lib/matplotlib/testing/decorators.py
@@ -204,6 +204,7 @@ def wrapper(*args, extension, request, **kwargs):
 
             if extension not in comparable_formats():
                 reason = {
+                    'gif': 'because ImageMagick is not installed',
                     'pdf': 'because Ghostscript is not installed',
                     'eps': 'because Ghostscript is not installed',
                     'svg': 'because Inkscape is not installed',
@@ -279,7 +280,7 @@ def image_comparison(baseline_images, extensions=None, tol=0,
     extensions : None or list of str
         The list of extensions to test, e.g. ``['png', 'pdf']``.
 
-        If *None*, defaults to all supported extensions: png, pdf, and svg.
+        If *None*, defaults to: png, pdf, and svg.
 
         When testing a single extension, it can be directly included in the
         names passed to *baseline_images*.  In that case, *extensions* must not
diff --git a/lib/matplotlib/tests/baseline_images/test_agg_filter/agg_filter_alpha.gif b/lib/matplotlib/tests/baseline_images/test_agg_filter/agg_filter_alpha.gif
new file mode 100644
index 000000000000..01a2d0bc288e
Binary files /dev/null and b/lib/matplotlib/tests/baseline_images/test_agg_filter/agg_filter_alpha.gif differ
diff --git a/lib/matplotlib/tests/test_agg.py b/lib/matplotlib/tests/test_agg.py
index 59387793605a..56b26904d041 100644
--- a/lib/matplotlib/tests/test_agg.py
+++ b/lib/matplotlib/tests/test_agg.py
@@ -263,6 +263,24 @@ def test_pil_kwargs_webp():
     assert buf_large.getbuffer().nbytes > buf_small.getbuffer().nbytes
 
 
+def test_gif_no_alpha():
+    plt.plot([0, 1, 2], [0, 1, 0])
+    buf = io.BytesIO()
+    plt.savefig(buf, format="gif", transparent=False)
+    im = Image.open(buf)
+    assert im.mode == "P"
+    assert im.info["transparency"] >= len(im.palette.colors)
+
+
+def test_gif_alpha():
+    plt.plot([0, 1, 2], [0, 1, 0])
+    buf = io.BytesIO()
+    plt.savefig(buf, format="gif", transparent=True)
+    im = Image.open(buf)
+    assert im.mode == "P"
+    assert im.info["transparency"] < len(im.palette.colors)
+
+
 @pytest.mark.skipif(not features.check("webp"), reason="WebP support not available")
 def test_webp_alpha():
     plt.plot([0, 1, 2], [0, 1, 0])
diff --git a/lib/matplotlib/tests/test_agg_filter.py b/lib/matplotlib/tests/test_agg_filter.py
index dc8cff6858ae..545e62d20d7c 100644
--- a/lib/matplotlib/tests/test_agg_filter.py
+++ b/lib/matplotlib/tests/test_agg_filter.py
@@ -5,7 +5,7 @@
 
 
 @image_comparison(baseline_images=['agg_filter_alpha'],
-                  extensions=['png', 'pdf'])
+                  extensions=['gif', 'png', 'pdf'])
 def test_agg_filter_alpha():
     # Remove this line when this test image is regenerated.
     plt.rcParams['pcolormesh.snap'] = False