diff --git a/docs/changelog.rst b/docs/changelog.rst
index 5f38876d..e117b506 100644
--- a/docs/changelog.rst
+++ b/docs/changelog.rst
@@ -43,6 +43,12 @@ Version TBD (unreleased)
   of storing a dangling C++ iterator reference in the returned Python
   iterator object. (PR `#788 <https://github.com/wjakob/nanobind/pull/788>`__)
 
+- Bindings for augmented assignment operators (as generated, for example, by
+  ``.def(nb::self += nb::self)``) now return the same object in Python in the
+  typical case where the C++ operator returns a reference to ``*this``.
+  Previously, after ``a += b``, ``a`` would be replaced with a copy.
+  (PR `#803 <https://github.com/wjakob/nanobind/pull/803>`__)
+
 Version 2.2.0 (October 3, 2024)
 -------------------------------
 
diff --git a/include/nanobind/operators.h b/include/nanobind/operators.h
index 55f8b068..e8ebb142 100644
--- a/include/nanobind/operators.h
+++ b/include/nanobind/operators.h
@@ -45,7 +45,7 @@ template <op_id id, op_type ot, typename L, typename R> struct op_ {
         using Lt = std::conditional_t<std::is_same_v<L, self_t>, Type, L>;
         using Rt = std::conditional_t<std::is_same_v<R, self_t>, Type, R>;
         using Op = op_impl<id, ot, Type, Lt, Rt>;
-        cl.def(Op::name(), &Op::execute, is_operator(), extra...);
+        cl.def(Op::name(), &Op::execute, is_operator(), Op::default_policy, extra...);
     }
 
     template <typename Class, typename... Extra> void execute_cast(Class &cl, const Extra&... extra) const {
@@ -53,17 +53,19 @@ template <op_id id, op_type ot, typename L, typename R> struct op_ {
         using Lt = std::conditional_t<std::is_same_v<L, self_t>, Type, L>;
         using Rt = std::conditional_t<std::is_same_v<R, self_t>, Type, R>;
         using Op = op_impl<id, ot, Type, Lt, Rt>;
-        cl.def(Op::name(), &Op::execute_cast, is_operator(), extra...);
+        cl.def(Op::name(), &Op::execute_cast, is_operator(), Op::default_policy, extra...);
     }
 };
 
 #define NB_BINARY_OPERATOR(id, rid, op, expr)                                          \
 template <typename B, typename L, typename R> struct op_impl<op_##id, op_l, B, L, R> { \
+    static constexpr rv_policy default_policy = rv_policy::automatic;                  \
     static char const* name() { return "__" #id "__"; }                                \
     static auto execute(const L &l, const R &r) -> decltype(expr) { return (expr); }   \
     static B execute_cast(const L &l, const R &r) { return B(expr); }                  \
 };                                                                                     \
 template <typename B, typename L, typename R> struct op_impl<op_##id, op_r, B, L, R> { \
+    static constexpr rv_policy default_policy = rv_policy::automatic;                  \
     static char const* name() { return "__" #rid "__"; }                               \
     static auto execute(const R &r, const L &l) -> decltype(expr) { return (expr); }   \
     static B execute_cast(const R &r, const L &l) { return B(expr); }                  \
@@ -80,6 +82,7 @@ template <typename T> op_<op_##id, op_r, T, self_t> op(const T &, const self_t &
 
 #define NB_INPLACE_OPERATOR(id, op, expr)                                              \
 template <typename B, typename L, typename R> struct op_impl<op_##id, op_l, B, L, R> { \
+    static constexpr rv_policy default_policy = rv_policy::move;                       \
     static char const* name() { return "__" #id "__"; }                                \
     static auto execute(L &l, const R &r) -> decltype(expr) { return expr; }           \
     static B execute_cast(L &l, const R &r) { return B(expr); }                        \
@@ -90,6 +93,7 @@ template <typename T> op_<op_##id, op_l, self_t, T> op(const self_t &, const T &
 
 #define NB_UNARY_OPERATOR(id, op, expr)                                                \
 template <typename B, typename L> struct op_impl<op_##id, op_u, B, L, undefined_t> {   \
+    static constexpr rv_policy default_policy = rv_policy::automatic;                  \
     static char const* name() { return "__" #id "__"; }                                \
     static auto execute(const L &l) -> decltype(expr) { return expr; }                 \
     static B execute_cast(const L &l) { return B(expr); }                              \
diff --git a/tests/test_classes.py b/tests/test_classes.py
index 42f755cd..cdf1939c 100644
--- a/tests/test_classes.py
+++ b/tests/test_classes.py
@@ -325,7 +325,9 @@ def test14_operators():
         assert repr(a - b) == "3"
     assert "unsupported operand type" in str(excinfo.value)
     assert repr(a - 2) == "-1"
+    a_before = id(a)
     a += b
+    assert id(a) == a_before
     assert repr(a) == "3"
     assert repr(b) == "2"