diff --git a/docs/source/error_code_list2.rst b/docs/source/error_code_list2.rst
index f160515f0a9e..673ac62b5058 100644
--- a/docs/source/error_code_list2.rst
+++ b/docs/source/error_code_list2.rst
@@ -62,6 +62,21 @@ Example:
          def __init__(self) -> None:
              self.value = 0
 
+Check that every function has a return annotation [no-incomplete-def]
+---------------------------------------------------------------------
+
+If you use :option:`--disallow-incomplete-defs <mypy --disallow-incomplete-defs>`, mypy requires that all functions
+fully annotated.
+
+Example:
+
+.. code-block:: python
+
+    # mypy: disallow-incomplete-defs
+
+    def example(x: int):  # Error: Function is missing a return type annotation  [no-incomplete-def]
+        pass
+
 Check that cast is not redundant [redundant-cast]
 -------------------------------------------------
 
diff --git a/mypy/checker.py b/mypy/checker.py
index 09dc0a726b99..bc4be0411ac6 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -1401,7 +1401,9 @@ def is_unannotated_any(t: Type) -> bool:
                     self.fail(message_registry.FUNCTION_TYPE_EXPECTED, fdef)
             elif isinstance(fdef.type, CallableType):
                 ret_type = get_proper_type(fdef.type.ret_type)
-                if is_unannotated_any(ret_type):
+                if is_unannotated_any(ret_type) and check_incomplete_defs:
+                    self.fail(message_registry.RETURN_TYPE_EXPECTED_INCOMPLETE_DEF, fdef)
+                elif is_unannotated_any(ret_type):
                     self.fail(message_registry.RETURN_TYPE_EXPECTED, fdef)
                 elif fdef.is_generator:
                     if is_unannotated_any(
@@ -1411,7 +1413,12 @@ def is_unannotated_any(t: Type) -> bool:
                 elif fdef.is_coroutine and isinstance(ret_type, Instance):
                     if is_unannotated_any(self.get_coroutine_return_type(ret_type)):
                         self.fail(message_registry.RETURN_TYPE_EXPECTED, fdef)
-                if any(is_unannotated_any(t) for t in fdef.type.arg_types):
+                if (
+                    any(is_unannotated_any(t) for t in fdef.type.arg_types)
+                    and check_incomplete_defs
+                ):
+                    self.fail(message_registry.ARGUMENT_TYPE_EXPECTED_INCOMPLETE_DEF, fdef)
+                elif any(is_unannotated_any(t) for t in fdef.type.arg_types):
                     self.fail(message_registry.ARGUMENT_TYPE_EXPECTED, fdef)
 
     def check___new___signature(self, fdef: FuncDef, typ: CallableType) -> None:
diff --git a/mypy/errorcodes.py b/mypy/errorcodes.py
index d274bb6dd5f0..a066635341e3 100644
--- a/mypy/errorcodes.py
+++ b/mypy/errorcodes.py
@@ -223,6 +223,11 @@ def __str__(self) -> str:
 )
 
 
+NO_INCOMPLETE_DEF: Final[ErrorCode] = ErrorCode(
+    "no-incomplete-def", "Function is missing a return type annotation", "General"
+)
+
+
 # Syntax errors are often blocking.
 SYNTAX: Final[ErrorCode] = ErrorCode("syntax", "Report syntax errors", "General")
 
diff --git a/mypy/message_registry.py b/mypy/message_registry.py
index b32edc06571a..d3e282fa3825 100644
--- a/mypy/message_registry.py
+++ b/mypy/message_registry.py
@@ -119,9 +119,15 @@ def with_additional_msg(self, info: str) -> ErrorMessage:
 RETURN_TYPE_EXPECTED: Final = ErrorMessage(
     "Function is missing a return type annotation", codes.NO_UNTYPED_DEF
 )
+RETURN_TYPE_EXPECTED_INCOMPLETE_DEF: Final = ErrorMessage(
+    "Function is missing a return type annotation", codes.NO_INCOMPLETE_DEF
+)
 ARGUMENT_TYPE_EXPECTED: Final = ErrorMessage(
     "Function is missing a type annotation for one or more arguments", codes.NO_UNTYPED_DEF
 )
+ARGUMENT_TYPE_EXPECTED_INCOMPLETE_DEF: Final = ErrorMessage(
+    "Function is missing a type annotation for one or more arguments", codes.NO_INCOMPLETE_DEF
+)
 KEYWORD_ARGUMENT_REQUIRES_STR_KEY_TYPE: Final = ErrorMessage(
     'Keyword argument only valid with "str" key type in call to "dict"'
 )
diff --git a/test-data/unit/check-errorcodes.test b/test-data/unit/check-errorcodes.test
index 33c8f7365375..34f22ee2399c 100644
--- a/test-data/unit/check-errorcodes.test
+++ b/test-data/unit/check-errorcodes.test
@@ -379,6 +379,15 @@ def f() -> None:
 def g():
     pass
 
+[case testErrorCodeNoReturnAnnotation]
+# flags: --disallow-incomplete-defs
+
+def f(i: int): # E: Function is missing a return type annotation  [no-incomplete-def]
+    pass
+
+def g(i) -> None: # E: Function is missing a type annotation for one or more arguments  [no-incomplete-def]
+    pass
+
 [case testErrorCodeIndexing]
 from typing import Dict
 x: Dict[int, int]