diff --git a/tensorflow/python/eager/def_function.py b/tensorflow/python/eager/def_function.py
index 6f50325015f..1ed603cab6a 100644
--- a/tensorflow/python/eager/def_function.py
+++ b/tensorflow/python/eager/def_function.py
@@ -422,6 +422,19 @@ class Function(object):
     self._input_signature = input_signature
     self._call_counter = _CallCounter(FREQUENT_TRACING_WARNING_MAX_CALL_HISTORY)
 
+  def __getstate__(self):
+    """Custom pickling, to omit unpickleable objects."""
+    result = self.__dict__.copy()
+    del result["_lock"]
+    del result["_descriptor_cache"]
+    return result
+
+  def __setstate__(self, state):
+    """Restore from pickled state."""
+    self.__dict__ = state
+    self._lock = threading.Lock()
+    self._descriptor_cache = weakref.WeakKeyDictionary()
+
   def _defun_with_scope(self, scope):
     """Creates a defun wrapped inside a variable creator scope."""
 
diff --git a/tensorflow/python/eager/def_function_test.py b/tensorflow/python/eager/def_function_test.py
index 998350f695d..6e23f25ec09 100644
--- a/tensorflow/python/eager/def_function_test.py
+++ b/tensorflow/python/eager/def_function_test.py
@@ -19,6 +19,7 @@ from __future__ import print_function
 
 import functools
 import itertools
+import pickle
 import re
 import weakref
 
@@ -68,6 +69,10 @@ class _ModelWithOptimizer(training.Model):
     return {'loss': loss}
 
 
+def undecorated_function(x):
+  return x * 3.
+
+
 class _HasDecoratedMethod(object):
 
   @def_function.function
@@ -747,6 +752,41 @@ class DefFunctionTest(test.TestCase, parameterized.TestCase):
     # If the graph is deleted, then an exception is raised on reading `captures`
     self.assertEmpty(graph.captures)
 
+  @parameterized.parameters(*itertools.product(
+      (None, (tensor_spec.TensorSpec([]),)),  # input_signature
+      (True, False),  # autograph
+      (None, converter.Feature.ALL),  # autograph_options
+      (None, 'foo.bar'),  # implements
+      (None, True, False),  # relax_shapes
+  ))
+  def test_pickle(self, input_signature, autograph, autograph_options,
+                  implements, relax_shapes):
+    """@function objects can be pickled and unpickled."""
+    # Can't pickle functions in __main__:
+    from tensorflow.python.eager.def_function_test import undecorated_function
+    original_py_function = undecorated_function
+
+    func = def_function.function(
+        func=original_py_function,
+        input_signature=input_signature,
+        autograph=autograph,
+        experimental_implements=implements,
+        experimental_autograph_options=autograph_options,
+        experimental_relax_shapes=relax_shapes,
+    )
+
+    cloned = pickle.loads(pickle.dumps(func))
+
+    self.assertEqual(func._name, cloned._name)
+    self.assertEqual(input_signature, cloned._input_signature)
+    self.assertEqual(autograph, cloned._autograph)
+    self.assertEqual(implements, cloned._implements)
+    self.assertEqual(autograph_options, cloned._experimental_autograph_options)
+    self.assertEqual(relax_shapes, cloned._experimental_relax_shapes)
+
+    x = array_ops.ones([])
+    self.assertEqual(self.evaluate(cloned(x)), self.evaluate(func(x)))
+
 
 if __name__ == '__main__':
   ops.enable_eager_execution()