diff --git a/homeassistant/components/knx/climate.py b/homeassistant/components/knx/climate.py
index 2d6a6686408..674e76d66e3 100644
--- a/homeassistant/components/knx/climate.py
+++ b/homeassistant/components/knx/climate.py
@@ -141,11 +141,20 @@ class KNXClimate(KnxEntity, ClimateEntity):
         """Initialize of a KNX climate device."""
         super().__init__(_create_climate(xknx, config))
         self._attr_entity_category = config.get(CONF_ENTITY_CATEGORY)
-        self._attr_supported_features = (
-            ClimateEntityFeature.TARGET_TEMPERATURE | ClimateEntityFeature.TURN_ON
-        )
+        self._attr_supported_features = ClimateEntityFeature.TARGET_TEMPERATURE
         if self._device.supports_on_off:
-            self._attr_supported_features |= ClimateEntityFeature.TURN_OFF
+            self._attr_supported_features |= (
+                ClimateEntityFeature.TURN_OFF | ClimateEntityFeature.TURN_ON
+            )
+        if (
+            self._device.mode is not None
+            and len(self._device.mode.controller_modes) >= 2
+            and HVACControllerMode.OFF in self._device.mode.controller_modes
+        ):
+            self._attr_supported_features |= (
+                ClimateEntityFeature.TURN_OFF | ClimateEntityFeature.TURN_ON
+            )
+
         if self.preset_modes:
             self._attr_supported_features |= ClimateEntityFeature.PRESET_MODE
         self._attr_target_temperature_step = self._device.temperature_step
@@ -158,6 +167,8 @@ class KNXClimate(KnxEntity, ClimateEntity):
         self.default_hvac_mode: HVACMode = config[
             ClimateSchema.CONF_DEFAULT_CONTROLLER_MODE
         ]
+        # non-OFF HVAC mode to be used when turning on the device without on_off address
+        self._last_hvac_mode: HVACMode = self.default_hvac_mode
 
     @property
     def current_temperature(self) -> float | None:
@@ -181,6 +192,34 @@ class KNXClimate(KnxEntity, ClimateEntity):
         temp = self._device.target_temperature_max
         return temp if temp is not None else super().max_temp
 
+    async def async_turn_on(self) -> None:
+        """Turn the entity on."""
+        if self._device.supports_on_off:
+            await self._device.turn_on()
+            self.async_write_ha_state()
+            return
+
+        if self._device.mode is not None and self._device.mode.supports_controller_mode:
+            knx_controller_mode = HVACControllerMode(
+                CONTROLLER_MODES_INV.get(self._last_hvac_mode)
+            )
+            await self._device.mode.set_controller_mode(knx_controller_mode)
+            self.async_write_ha_state()
+
+    async def async_turn_off(self) -> None:
+        """Turn the entity off."""
+        if self._device.supports_on_off:
+            await self._device.turn_off()
+            self.async_write_ha_state()
+            return
+
+        if (
+            self._device.mode is not None
+            and HVACControllerMode.OFF in self._device.mode.controller_modes
+        ):
+            await self._device.mode.set_controller_mode(HVACControllerMode.OFF)
+            self.async_write_ha_state()
+
     async def async_set_temperature(self, **kwargs: Any) -> None:
         """Set new target temperature."""
         temperature = kwargs.get(ATTR_TEMPERATURE)
@@ -194,9 +233,12 @@ class KNXClimate(KnxEntity, ClimateEntity):
         if self._device.supports_on_off and not self._device.is_on:
             return HVACMode.OFF
         if self._device.mode is not None and self._device.mode.supports_controller_mode:
-            return CONTROLLER_MODES.get(
+            hvac_mode = CONTROLLER_MODES.get(
                 self._device.mode.controller_mode.value, self.default_hvac_mode
             )
+            if hvac_mode is not HVACMode.OFF:
+                self._last_hvac_mode = hvac_mode
+            return hvac_mode
         return self.default_hvac_mode
 
     @property
@@ -234,21 +276,23 @@ class KNXClimate(KnxEntity, ClimateEntity):
         return None
 
     async def async_set_hvac_mode(self, hvac_mode: HVACMode) -> None:
-        """Set operation mode."""
-        if self._device.supports_on_off and hvac_mode == HVACMode.OFF:
-            await self._device.turn_off()
-        else:
-            if self._device.supports_on_off and not self._device.is_on:
-                await self._device.turn_on()
-            if (
-                self._device.mode is not None
-                and self._device.mode.supports_controller_mode
-            ):
-                knx_controller_mode = HVACControllerMode(
-                    CONTROLLER_MODES_INV.get(hvac_mode)
-                )
+        """Set controller mode."""
+        if self._device.mode is not None and self._device.mode.supports_controller_mode:
+            knx_controller_mode = HVACControllerMode(
+                CONTROLLER_MODES_INV.get(hvac_mode)
+            )
+            if knx_controller_mode in self._device.mode.controller_modes:
                 await self._device.mode.set_controller_mode(knx_controller_mode)
-        self.async_write_ha_state()
+                self.async_write_ha_state()
+                return
+
+        if self._device.supports_on_off:
+            if hvac_mode == HVACMode.OFF:
+                await self._device.turn_off()
+            elif not self._device.is_on:
+                # for default hvac mode, otherwise above would have triggered
+                await self._device.turn_on()
+            self.async_write_ha_state()
 
     @property
     def preset_mode(self) -> str | None:
diff --git a/tests/components/knx/test_climate.py b/tests/components/knx/test_climate.py
index 240fde9ee8b..c81a6fccf15 100644
--- a/tests/components/knx/test_climate.py
+++ b/tests/components/knx/test_climate.py
@@ -1,5 +1,7 @@
 """Test KNX climate."""
 
+import pytest
+
 from homeassistant.components.climate import PRESET_ECO, PRESET_SLEEP, HVACMode
 from homeassistant.components.knx.schema import ClimateSchema
 from homeassistant.const import CONF_NAME, STATE_IDLE
@@ -52,6 +54,94 @@ async def test_climate_basic_temperature_set(
     assert len(events) == 1
 
 
+@pytest.mark.parametrize("heat_cool", [False, True])
+async def test_climate_on_off(
+    hass: HomeAssistant, knx: KNXTestKit, heat_cool: bool
+) -> None:
+    """Test KNX climate on/off."""
+    await knx.setup_integration(
+        {
+            ClimateSchema.PLATFORM: {
+                CONF_NAME: "test",
+                ClimateSchema.CONF_TEMPERATURE_ADDRESS: "1/2/3",
+                ClimateSchema.CONF_TARGET_TEMPERATURE_ADDRESS: "1/2/4",
+                ClimateSchema.CONF_TARGET_TEMPERATURE_STATE_ADDRESS: "1/2/5",
+                ClimateSchema.CONF_ON_OFF_ADDRESS: "1/2/8",
+                ClimateSchema.CONF_ON_OFF_STATE_ADDRESS: "1/2/9",
+            }
+            | (
+                {
+                    ClimateSchema.CONF_HEAT_COOL_ADDRESS: "1/2/10",
+                    ClimateSchema.CONF_HEAT_COOL_STATE_ADDRESS: "1/2/11",
+                }
+                if heat_cool
+                else {}
+            )
+        }
+    )
+
+    await hass.async_block_till_done()
+    # read heat/cool state
+    if heat_cool:
+        await knx.assert_read("1/2/11")
+        await knx.receive_response("1/2/11", 0)  # cool
+    # read temperature state
+    await knx.assert_read("1/2/3")
+    await knx.receive_response("1/2/3", RAW_FLOAT_20_0)
+    # read target temperature state
+    await knx.assert_read("1/2/5")
+    await knx.receive_response("1/2/5", RAW_FLOAT_22_0)
+    # read on/off state
+    await knx.assert_read("1/2/9")
+    await knx.receive_response("1/2/9", 1)
+
+    # turn off
+    await hass.services.async_call(
+        "climate",
+        "turn_off",
+        {"entity_id": "climate.test"},
+        blocking=True,
+    )
+    await knx.assert_write("1/2/8", 0)
+    assert hass.states.get("climate.test").state == "off"
+
+    # turn on
+    await hass.services.async_call(
+        "climate",
+        "turn_on",
+        {"entity_id": "climate.test"},
+        blocking=True,
+    )
+    await knx.assert_write("1/2/8", 1)
+    if heat_cool:
+        # does not fall back to default hvac mode after turn_on
+        assert hass.states.get("climate.test").state == "cool"
+    else:
+        assert hass.states.get("climate.test").state == "heat"
+
+    # set hvac mode to off triggers turn_off if no controller_mode is available
+    await hass.services.async_call(
+        "climate",
+        "set_hvac_mode",
+        {"entity_id": "climate.test", "hvac_mode": HVACMode.OFF},
+        blocking=True,
+    )
+    await knx.assert_write("1/2/8", 0)
+
+    # set hvac mode to heat
+    await hass.services.async_call(
+        "climate",
+        "set_hvac_mode",
+        {"entity_id": "climate.test", "hvac_mode": HVACMode.HEAT},
+        blocking=True,
+    )
+    if heat_cool:
+        # only set new hvac_mode without changing on/off - actuator shall handle that
+        await knx.assert_write("1/2/10", 1)
+    else:
+        await knx.assert_write("1/2/8", 1)
+
+
 async def test_climate_hvac_mode(hass: HomeAssistant, knx: KNXTestKit) -> None:
     """Test KNX climate hvac mode."""
     await knx.setup_integration(
@@ -68,7 +158,6 @@ async def test_climate_hvac_mode(hass: HomeAssistant, knx: KNXTestKit) -> None:
             }
         }
     )
-    async_capture_events(hass, "state_changed")
 
     await hass.async_block_till_done()
     # read states state updater
@@ -82,14 +171,14 @@ async def test_climate_hvac_mode(hass: HomeAssistant, knx: KNXTestKit) -> None:
     await knx.assert_read("1/2/5")
     await knx.receive_response("1/2/5", RAW_FLOAT_22_0)
 
-    # turn hvac off
+    # turn hvac mode to off
     await hass.services.async_call(
         "climate",
         "set_hvac_mode",
         {"entity_id": "climate.test", "hvac_mode": HVACMode.OFF},
         blocking=True,
     )
-    await knx.assert_write("1/2/8", False)
+    await knx.assert_write("1/2/6", (0x06,))
 
     # turn hvac on
     await hass.services.async_call(
@@ -98,7 +187,6 @@ async def test_climate_hvac_mode(hass: HomeAssistant, knx: KNXTestKit) -> None:
         {"entity_id": "climate.test", "hvac_mode": HVACMode.HEAT},
         blocking=True,
     )
-    await knx.assert_write("1/2/8", True)
     await knx.assert_write("1/2/6", (0x01,))
 
 
@@ -182,7 +270,6 @@ async def test_update_entity(hass: HomeAssistant, knx: KNXTestKit) -> None:
     )
     assert await async_setup_component(hass, "homeassistant", {})
     await hass.async_block_till_done()
-    async_capture_events(hass, "state_changed")
 
     await hass.async_block_till_done()
     # read states state updater