diff --git a/Lib/functools.py b/Lib/functools.py
index 836eb680ccd4d4..7ed3d67f3cf79c 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -19,7 +19,7 @@
 # import weakref  # Deferred to single_dispatch()
 from operator import itemgetter
 from reprlib import recursive_repr
-from types import GenericAlias, MethodType, MappingProxyType, UnionType
+from types import FunctionType, GenericAlias, MethodType, MappingProxyType, UnionType
 from _thread import RLock
 
 ################################################################################
@@ -888,6 +888,48 @@ def _find_impl(cls, registry):
             match = t
     return registry.get(match)
 
+def _get_singledispatch_annotated_param(func, *, _inside_dispatchmethod=False):
+    """Finds the first positional and user-specified parameter in a callable
+    or descriptor.
+
+    Used by singledispatch for registration by type annotation of the parameter.
+    """
+    # Pick the first parameter if function had @staticmethod.
+    if isinstance(func, staticmethod):
+        idx = 0
+        func = func.__func__
+    # Pick the second parameter if function had @classmethod or is a bound method.
+    elif isinstance(func, (classmethod, MethodType)):
+        idx = 1
+        func = func.__func__
+    # If it is a regular function:
+    # Pick the first parameter if registering via singledispatch.
+    # Pick the second parameter if registering via singledispatchmethod.
+    else:
+        idx = int(_inside_dispatchmethod)
+
+    # If it is a simple function, try to read from the code object fast.
+    if isinstance(func, FunctionType) and not hasattr(func, "__wrapped__"):
+        # Emulate inspect._signature_from_function to get the desired parameter.
+        func_code = func.__code__
+        try:
+            return func_code.co_varnames[:func_code.co_argcount][idx]
+        except IndexError:
+            pass
+
+    # Fall back to inspect.signature (slower, but complete).
+    import inspect
+    params = list(inspect.signature(func).parameters.values())
+    try:
+        param = params[idx]
+    except IndexError:
+        pass
+    else:
+        # Allow variadic positional "(*args)" parameters for backward compatibility.
+        if param.kind not in (inspect.Parameter.KEYWORD_ONLY, inspect.Parameter.VAR_KEYWORD):
+            return param.name
+    return None
+
 def singledispatch(func):
     """Single-dispatch generic function decorator.
 
@@ -935,7 +977,7 @@ def _is_valid_dispatch_type(cls):
         return (isinstance(cls, UnionType) and
                 all(isinstance(arg, type) for arg in cls.__args__))
 
-    def register(cls, func=None):
+    def register(cls, func=None, _inside_dispatchmethod=False):
         """generic_func.register(cls, func) -> func
 
         Registers a new implementation for the given *cls* on a *generic_func*.
@@ -960,10 +1002,28 @@ def register(cls, func=None):
                 )
             func = cls
 
+            argname = _get_singledispatch_annotated_param(
+                func, _inside_dispatchmethod=_inside_dispatchmethod)
+            if argname is None:
+                raise TypeError(
+                    f"Invalid first argument to `register()`: {func!r} "
+                    f"does not accept positional arguments."
+                )
+
             # only import typing if annotation parsing is necessary
             from typing import get_type_hints
             from annotationlib import Format, ForwardRef
-            argname, cls = next(iter(get_type_hints(func, format=Format.FORWARDREF).items()))
+            annotations = get_type_hints(func, format=Format.FORWARDREF)
+
+            try:
+                cls = annotations[argname]
+            except KeyError:
+                raise TypeError(
+                    f"Invalid first argument to `register()`: {func!r}. "
+                    "Use either `@register(some_class)` or add a type "
+                    f"annotation to parameter {argname!r} of your callable."
+                ) from None
+
             if not _is_valid_dispatch_type(cls):
                 if isinstance(cls, UnionType):
                     raise TypeError(
@@ -1027,7 +1087,7 @@ def register(self, cls, method=None):
 
         Registers a new implementation for the given *cls* on a *generic_method*.
         """
-        return self.dispatcher.register(cls, func=method)
+        return self.dispatcher.register(cls, func=method, _inside_dispatchmethod=True)
 
     def __get__(self, obj, cls=None):
         return _singledispatchmethod_get(self, obj, cls)
diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index 94b469397139c7..4b1a2b3e12ad35 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -2905,13 +2905,34 @@ def t(self, arg):
             def _(self, arg: int):
                 return "int"
             @t.register
-            def _(self, arg: str):
+            def _(self, arg: complex, /):
+                return "complex"
+            @t.register
+            def _(self, /, arg: str):
                 return "str"
+            # See GH-130827.
+            def wrapped1(self: typing.Self, arg: bytes):
+                return "bytes"
+            @t.register
+            @functools.wraps(wrapped1)
+            def wrapper1(self, *args, **kwargs):
+                return self.wrapped1(*args, **kwargs)
+
+            def wrapped2(self, arg: bytearray) -> str:
+                return "bytearray"
+            @t.register
+            @functools.wraps(wrapped2)
+            def wrapper2(self, *args: typing.Any, **kwargs: typing.Any):
+                return self.wrapped2(*args, **kwargs)
+
         a = A()
 
         self.assertEqual(a.t(0), "int")
+        self.assertEqual(a.t(0j), "complex")
         self.assertEqual(a.t(''), "str")
         self.assertEqual(a.t(0.0), "base")
+        self.assertEqual(a.t(b''), "bytes")
+        self.assertEqual(a.t(bytearray()), "bytearray")
 
     def test_staticmethod_type_ann_register(self):
         class A:
@@ -3172,12 +3193,27 @@ def test_invalid_registrations(self):
         @functools.singledispatch
         def i(arg):
             return "base"
+        with self.assertRaises(TypeError) as exc:
+            @i.register
+            def _() -> None:
+                return "My function doesn't take arguments"
+        self.assertStartsWith(str(exc.exception), msg_prefix)
+        self.assertEndsWith(str(exc.exception), "does not accept positional arguments.")
+
+        with self.assertRaises(TypeError) as exc:
+            @i.register
+            def _(*, foo: str) -> None:
+                return "My function takes keyword-only arguments"
+        self.assertStartsWith(str(exc.exception), msg_prefix)
+        self.assertEndsWith(str(exc.exception), "does not accept positional arguments.")
+
         with self.assertRaises(TypeError) as exc:
             @i.register(42)
             def _(arg):
                 return "I annotated with a non-type"
         self.assertStartsWith(str(exc.exception), msg_prefix + "42")
         self.assertEndsWith(str(exc.exception), msg_suffix)
+
         with self.assertRaises(TypeError) as exc:
             @i.register
             def _(arg):
@@ -3187,6 +3223,33 @@ def _(arg):
         )
         self.assertEndsWith(str(exc.exception), msg_suffix)
 
+        with self.assertRaises(TypeError) as exc:
+            @i.register
+            def _(arg, extra: int):
+                return "I did not annotate the right param"
+        self.assertStartsWith(str(exc.exception), msg_prefix +
+            "<function TestSingleDispatch.test_invalid_registrations.<locals>._"
+        )
+        self.assertEndsWith(str(exc.exception),
+            "Use either `@register(some_class)` or add a type annotation "
+            f"to parameter 'arg' of your callable.")
+
+        with self.assertRaises(TypeError) as exc:
+            # See GH-84644.
+
+            @functools.singledispatch
+            def func(arg):...
+
+            @func.register
+            def _int(arg) -> int:...
+
+        self.assertStartsWith(str(exc.exception), msg_prefix +
+            "<function TestSingleDispatch.test_invalid_registrations.<locals>._int"
+        )
+        self.assertEndsWith(str(exc.exception),
+            "Use either `@register(some_class)` or add a type annotation "
+            f"to parameter 'arg' of your callable.")
+
         with self.assertRaises(TypeError) as exc:
             @i.register
             def _(arg: typing.Iterable[str]):
diff --git a/Misc/NEWS.d/next/Library/2026-01-06-09-13-53.gh-issue-84644.V_cYP3.rst b/Misc/NEWS.d/next/Library/2026-01-06-09-13-53.gh-issue-84644.V_cYP3.rst
new file mode 100644
index 00000000000000..95190f88b16e60
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-01-06-09-13-53.gh-issue-84644.V_cYP3.rst
@@ -0,0 +1,5 @@
+:func:`functools.singledispatch` and :func:`functools.singledispatchmethod`
+now require callables to be correctly annotated if registering without a type explicitly
+specified in the decorator. The first user-specified positional parameter of a callable
+must always be annotated. Before, a callable could be registered based on its return type
+annotation or based on an irrelevant parameter type annotation. Contributed by Bartosz Sławecki.