diff --git a/src/attr/__init__.py b/src/attr/__init__.py
--- a/src/attr/__init__.py
+++ b/src/attr/__init__.py
@@ -10,7 +10,7 @@
 from . import converters, exceptions, filters, setters, validators
 from ._cmp import cmp_using
 from ._config import get_run_validators, set_run_validators
-from ._funcs import asdict, assoc, astuple, evolve, has, resolve_types
+from ._funcs import asdict, assoc, astuple, has, resolve_types
 from ._make import (
     NOTHING,
     Attribute,
@@ -19,6 +19,7 @@
     _Nothing,
     attrib,
     attrs,
+    evolve,
     fields,
     fields_dict,
     make_class,
diff --git a/src/attr/_funcs.py b/src/attr/_funcs.py
--- a/src/attr/_funcs.py
+++ b/src/attr/_funcs.py
@@ -394,60 +394,6 @@ def assoc(inst, **changes):
     return new
 
 
-def evolve(*args, **changes):
-    """
-    Create a new instance, based on the first positional argument with
-    *changes* applied.
-
-    Args:
-
-        inst:
-            Instance of a class with *attrs* attributes. *inst* must be passed
-            as a positional argument.
-
-        changes:
-            Keyword changes in the new copy.
-
-    Returns:
-        A copy of inst with *changes* incorporated.
-
-    Raises:
-        TypeError:
-            If *attr_name* couldn't be found in the class ``__init__``.
-
-        attrs.exceptions.NotAnAttrsClassError:
-            If *cls* is not an *attrs* class.
-
-    .. versionadded:: 17.1.0
-    .. deprecated:: 23.1.0
-       It is now deprecated to pass the instance using the keyword argument
-       *inst*. It will raise a warning until at least April 2024, after which
-       it will become an error. Always pass the instance as a positional
-       argument.
-    .. versionchanged:: 24.1.0
-       *inst* can't be passed as a keyword argument anymore.
-    """
-    try:
-        (inst,) = args
-    except ValueError:
-        msg = (
-            f"evolve() takes 1 positional argument, but {len(args)} were given"
-        )
-        raise TypeError(msg) from None
-
-    cls = inst.__class__
-    attrs = fields(cls)
-    for a in attrs:
-        if not a.init:
-            continue
-        attr_name = a.name  # To deal with private attributes.
-        init_name = a.alias
-        if init_name not in changes:
-            changes[init_name] = getattr(inst, attr_name)
-
-    return cls(**changes)
-
-
 def resolve_types(
     cls, globalns=None, localns=None, attribs=None, include_extras=True
 ):
diff --git a/src/attr/_make.py b/src/attr/_make.py
--- a/src/attr/_make.py
+++ b/src/attr/_make.py
@@ -22,6 +22,7 @@
 from ._compat import (
     PY_3_10_PLUS,
     PY_3_11_PLUS,
+    PY_3_13_PLUS,
     _AnnotationExtractor,
     _get_annotations,
     get_generic_base,
@@ -565,6 +566,64 @@ def _frozen_delattrs(self, name):
     raise FrozenInstanceError
 
 
+def evolve(*args, **changes):
+    """
+    Create a new instance, based on the first positional argument with
+    *changes* applied.
+
+    .. tip::
+
+       On Python 3.13 and later, you can also use `copy.replace` instead.
+
+    Args:
+
+        inst:
+            Instance of a class with *attrs* attributes. *inst* must be passed
+            as a positional argument.
+
+        changes:
+            Keyword changes in the new copy.
+
+    Returns:
+        A copy of inst with *changes* incorporated.
+
+    Raises:
+        TypeError:
+            If *attr_name* couldn't be found in the class ``__init__``.
+
+        attrs.exceptions.NotAnAttrsClassError:
+            If *cls* is not an *attrs* class.
+
+    .. versionadded:: 17.1.0
+    .. deprecated:: 23.1.0
+       It is now deprecated to pass the instance using the keyword argument
+       *inst*. It will raise a warning until at least April 2024, after which
+       it will become an error. Always pass the instance as a positional
+       argument.
+    .. versionchanged:: 24.1.0
+       *inst* can't be passed as a keyword argument anymore.
+    """
+    try:
+        (inst,) = args
+    except ValueError:
+        msg = (
+            f"evolve() takes 1 positional argument, but {len(args)} were given"
+        )
+        raise TypeError(msg) from None
+
+    cls = inst.__class__
+    attrs = fields(cls)
+    for a in attrs:
+        if not a.init:
+            continue
+        attr_name = a.name  # To deal with private attributes.
+        init_name = a.alias
+        if init_name not in changes:
+            changes[init_name] = getattr(inst, attr_name)
+
+    return cls(**changes)
+
+
 class _ClassBuilder:
     """
     Iteratively build *one* class.
@@ -979,6 +1038,12 @@ def add_init(self):
 
         return self
 
+    def add_replace(self):
+        self._cls_dict["__replace__"] = self._add_method_dunders(
+            lambda self, **changes: evolve(self, **changes)
+        )
+        return self
+
     def add_match_args(self):
         self._cls_dict["__match_args__"] = tuple(
             field.name
@@ -1381,6 +1446,9 @@ def wrap(cls):
                 msg = "Invalid value for cache_hash.  To use hash caching, init must be True."
                 raise TypeError(msg)
 
+        if PY_3_13_PLUS and not _has_own_attribute(cls, "__replace__"):
+            builder.add_replace()
+
         if (
             PY_3_10_PLUS
             and match_args
@@ -2394,7 +2462,7 @@ def evolve(self, **changes):
         Copy *self* and apply *changes*.
 
         This works similarly to `attrs.evolve` but that function does not work
-        with {class}`Attribute`.
+        with :class:`attrs.Attribute`.
 
         It is mainly meant to be used for `transform-fields`.
 
diff --git a/src/attr/_next_gen.py b/src/attr/_next_gen.py
--- a/src/attr/_next_gen.py
+++ b/src/attr/_next_gen.py
@@ -316,6 +316,9 @@ def define(
        If a class has an *inherited* classmethod called
        ``__attrs_init_subclass__``, it is executed after the class is created.
     .. deprecated:: 24.1.0 *hash* is deprecated in favor of *unsafe_hash*.
+    .. versionadded:: 24.3.0
+       Unless already present, a ``__replace__`` method is automatically
+       created for `copy.replace` (Python 3.13+ only).
 
     .. note::
 

diff --git a/tests/test_functional.py b/tests/test_functional.py
--- a/tests/test_functional.py
+++ b/tests/test_functional.py
@@ -4,6 +4,7 @@
 End-to-end tests.
 """
 
+import copy
 import inspect
 import pickle
 
@@ -16,6 +17,7 @@
 
 import attr
 
+from attr._compat import PY_3_13_PLUS
 from attr._make import NOTHING, Attribute
 from attr.exceptions import FrozenInstanceError
 
@@ -766,3 +768,40 @@ class ToRegister(Base):
             pass
 
         assert [ToRegister] == REGISTRY
+
+
+@pytest.mark.skipif(not PY_3_13_PLUS, reason="requires Python 3.13+")
+class TestReplace:
+    def test_replaces(self):
+        """
+        copy.replace() is added by default and works like `attrs.evolve`.
+        """
+        inst = C1(1, 2)
+
+        assert C1(1, 42) == copy.replace(inst, y=42)
+        assert C1(42, 2) == copy.replace(inst, x=42)
+
+    def test_already_has_one(self):
+        """
+        If the object already has a __replace__, it's left alone.
+        """
+        sentinel = object()
+
+        @attr.s
+        class C:
+            x = attr.ib()
+
+            __replace__ = sentinel
+
+        assert sentinel == C.__replace__
+
+    def test_invalid_field_name(self):
+        """
+        Invalid field names raise a TypeError.
+
+        This is consistent with dataclasses.
+        """
+        inst = C1(1, 2)
+
+        with pytest.raises(TypeError):
+            copy.replace(inst, z=42)

`copy.replace` support
Python 3.13 introduced the `__replace__` dunder, exposed via [`copy.replace`](https://docs.python.org/3.13/library/copy.html#copy.replace), as a [generalised method](https://discuss.python.org/t/generalize-replace-function/28511) through which to replace fields in immutable dataclass-likes.  Would you be interested in supporting it in addition to attrs' own `evolve`?

Yeah, that sounds super cool!