diff --git a/mypy/checker.py b/mypy/checker.py
index 8e4af18c17c3..109fc24043bd 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -59,6 +59,7 @@
 from mypy.meet import is_overlapping_types
 from mypy.options import Options
 from mypy.plugin import Plugin, CheckerPluginInterface
+from mypy.sharedparse import BINARY_MAGIC_METHODS
 
 from mypy import experiments
 
@@ -2179,8 +2180,11 @@ def check_return_stmt(self, s: ReturnStmt) -> None:
                 if isinstance(typ, AnyType):
                     # (Unless you asked to be warned in that case, and the
                     # function is not declared to return Any)
-                    if (self.options.warn_return_any and not self.current_node_deferred and
-                            not is_proper_subtype(AnyType(TypeOfAny.special_form), return_type)):
+                    if (self.options.warn_return_any
+                        and not self.current_node_deferred
+                        and not is_proper_subtype(AnyType(TypeOfAny.special_form), return_type)
+                        and not (defn.name() in BINARY_MAGIC_METHODS and
+                                 is_literal_not_implemented(s.expr))):
                         self.msg.incorrectly_returning_any(return_type, s)
                     return
 
@@ -3232,6 +3236,10 @@ def remove_optional(typ: Type) -> Type:
         return typ
 
 
+def is_literal_not_implemented(n: Expression) -> bool:
+    return isinstance(n, NameExpr) and n.fullname == 'builtins.NotImplemented'
+
+
 def builtin_item_type(tp: Type) -> Optional[Type]:
     """Get the item type of a builtin container.
 
diff --git a/mypy/sharedparse.py b/mypy/sharedparse.py
index 1b3e5a3a9460..91015b6d693f 100644
--- a/mypy/sharedparse.py
+++ b/mypy/sharedparse.py
@@ -16,7 +16,6 @@
     "__delitem__",
     "__divmod__",
     "__div__",
-    "__divmod__",
     "__enter__",
     "__exit__",
     "__eq__",
@@ -92,6 +91,52 @@
 
 MAGIC_METHODS_POS_ARGS_ONLY = MAGIC_METHODS - MAGIC_METHODS_ALLOWING_KWARGS
 
+BINARY_MAGIC_METHODS = {
+    "__add__",
+    "__and__",
+    "__cmp__",
+    "__divmod__",
+    "__div__",
+    "__eq__",
+    "__floordiv__",
+    "__ge__",
+    "__gt__",
+    "__iadd__",
+    "__iand__",
+    "__idiv__",
+    "__ifloordiv__",
+    "__ilshift__",
+    "__imod__",
+    "__imul__",
+    "__ior__",
+    "__ipow__",
+    "__irshift__",
+    "__isub__",
+    "__ixor__",
+    "__le__",
+    "__lshift__",
+    "__lt__",
+    "__mod__",
+    "__mul__",
+    "__or__",
+    "__pow__",
+    "__radd__",
+    "__rand__",
+    "__rdiv__",
+    "__rfloordiv__",
+    "__rlshift__",
+    "__rmod__",
+    "__rmul__",
+    "__ror__",
+    "__rpow__",
+    "__rrshift__",
+    "__rshift__",
+    "__rsub__",
+    "__rxor__",
+    "__sub__",
+    "__xor__",
+}
+
 
 def special_function_elide_names(name: str) -> bool:
     return name in MAGIC_METHODS_POS_ARGS_ONLY
diff --git a/test-data/unit/check-warnings.test b/test-data/unit/check-warnings.test
index 4acbfe69df80..d812ed83efa8 100644
--- a/test-data/unit/check-warnings.test
+++ b/test-data/unit/check-warnings.test
@@ -143,6 +143,21 @@ def f() -> int: return g()
 [out]
 main:4: warning: Returning Any from function declared to return "int"
 
+[case testReturnAnyForNotImplementedInBinaryMagicMethods]
+# flags: --warn-return-any
+class A:
+    def __eq__(self, other: object) -> bool: return NotImplemented
+[builtins fixtures/notimplemented.pyi]
+[out]
+
+[case testReturnAnyForNotImplementedInNormalMethods]
+# flags: --warn-return-any
+class A:
+    def some(self) -> bool: return NotImplemented
+[builtins fixtures/notimplemented.pyi]
+[out]
+main:3: warning: Returning Any from function declared to return "bool"
+
 [case testReturnAnyFromTypedFunctionWithSpecificFormatting]
 # flags: --warn-return-any
 from typing import Any, Tuple
diff --git a/test-data/unit/fixtures/notimplemented.pyi b/test-data/unit/fixtures/notimplemented.pyi
new file mode 100644
index 000000000000..e619a6c5ad85
--- /dev/null
+++ b/test-data/unit/fixtures/notimplemented.pyi
@@ -0,0 +1,13 @@
+# builtins stub used in NotImplemented related cases.
+from typing import Any, cast
+
+
+class object:
+    def __init__(self) -> None: pass
+
+class type: pass
+class function: pass
+class bool: pass
+class int: pass
+class str: pass
+NotImplemented = cast(Any, None)