diff --git a/Lib/contextlib.py b/Lib/contextlib.py
index bde2feb..2bf83fb 100644
--- a/Lib/contextlib.py
+++ b/Lib/contextlib.py
@@ -3,6 +3,7 @@
 import sys
 from collections import deque
 from functools import wraps
+from inspect import signature
 
 __all__ = ["contextmanager", "closing", "ContextDecorator", "ExitStack"]
 
@@ -196,6 +197,25 @@ class ExitStack(object):
 
         Cannot suppress exceptions.
         """
+        # Let's check if the callback accepts `*args` and `**kwds`.
+        # First we get a signature of it, which may fail with a
+        # TypeError if the object is not callable or with a ValueError
+        # if 'signature()' does not support it (builtin)
+        try:
+            sig = signature(callback)
+        except ValueError:
+            # The callback is a built-in function or type, hence
+            # we can't do any validation
+            pass
+        else:
+            # Second, we try to bind the passed callback arguments
+            try:
+                sig.bind(*args, **kwds)
+            except TypeError:
+                msg = ('{!r} callback does not accept the passed '
+                       'arguments'.format(callback))
+                raise TypeError(msg) from None
+
         def _exit_wrapper(exc_type, exc, tb):
             callback(*args, **kwds)
         # We changed the signature, so using @wraps is not appropriate, but
diff --git a/Lib/test/test_contextlib.py b/Lib/test/test_contextlib.py
index e52ed91..25a5b9d 100644
--- a/Lib/test/test_contextlib.py
+++ b/Lib/test/test_contextlib.py
@@ -585,6 +585,16 @@ class TestExitStack(unittest.TestCase):
             for i in range(10000):
                 stack.callback(int)
 
+    def test_callback_incorrect_arguments(self):
+        with ExitStack() as stack:
+            with self.assertRaisesRegexp(TypeError, 'the passed arguments'):
+                stack.callback((lambda a, b: None), 1, 2, 3)
+
+    def test_callback_not_callable(self):
+        with ExitStack() as stack:
+            with self.assertRaisesRegexp(TypeError, 'is not a callable'):
+                stack.callback(42)
+
     def test_instance_bypass(self):
         class Example(object): pass
         cm = Example()