diff --git a/homeassistant/components/sensor/recorder.py b/homeassistant/components/sensor/recorder.py
index 78c5719510aa3..8499b610659e3 100644
--- a/homeassistant/components/sensor/recorder.py
+++ b/homeassistant/components/sensor/recorder.py
@@ -94,6 +94,8 @@ class _StatisticsConfig:
 # Keep track of entities for which a warning about unsupported unit has been logged
 WARN_UNSUPPORTED_UNIT: HassKey[set[str]] = HassKey(f"{DOMAIN}_warn_unsupported_unit")
 WARN_UNSTABLE_UNIT: HassKey[set[str]] = HassKey(f"{DOMAIN}_warn_unstable_unit")
+# Keep track of entities for which a change in unit has been observed
+SEEN_CHANGED_UNIT: HassKey[set[str]] = HassKey(f"{DOMAIN}_seen_changed_unit")
 # Keep track of entities for which a warning about statistics mean algorithm change has been logged
 WARN_STATISTICS_MEAN_CHANGED: HassKey[set[str]] = HassKey(
     f"{DOMAIN}_warn_statistics_mean_change"
@@ -279,11 +281,12 @@ def _normalize_states(
     """Normalize units."""
     state_unit: str | None = None
     statistics_unit: str | None
-    state_unit = fstates[0][1].attributes.get(ATTR_UNIT_OF_MEASUREMENT)
-    device_class = fstates[0][1].attributes.get(ATTR_DEVICE_CLASS)
+    state_unit = fstates[-1][1].attributes.get(ATTR_UNIT_OF_MEASUREMENT)
+    all_units = _get_units(fstates)
+    device_class = fstates[-1][1].attributes.get(ATTR_DEVICE_CLASS)
     old_metadata = old_metadatas[entity_id][1] if entity_id in old_metadatas else None
     if not old_metadata:
-        # We've not seen this sensor before, the first valid state determines the unit
+        # We've not seen this sensor before, the most recent valid state determines the unit
         # used for statistics
         statistics_unit = state_unit
         unit_class = _get_unit_class(device_class, state_unit)
@@ -305,7 +308,6 @@ def _normalize_states(
     if not (converter := _get_unit_converter(unit_class)):
         # The unit used by this sensor doesn't support unit conversion
 
-        all_units = _get_units(fstates)
         if not _equivalent_units(all_units):
             if WARN_UNSTABLE_UNIT not in hass.data:
                 hass.data[WARN_UNSTABLE_UNIT] = set()
@@ -332,20 +334,34 @@ def _normalize_states(
 
         if state_unit != statistics_unit:
             unit_class = _get_unit_class(
-                fstates[0][1].attributes.get(ATTR_DEVICE_CLASS),
+                fstates[-1][1].attributes.get(ATTR_DEVICE_CLASS),
                 state_unit,
             )
         return unit_class, state_unit, fstates
 
-    valid_fstates: list[tuple[float, State]] = []
-    convert: Callable[[float], float] | None = None
-    last_unit: str | None | UndefinedType = UNDEFINED
     valid_units = converter.VALID_UNITS
 
-    for fstate, state in fstates:
-        state_unit = state.attributes.get(ATTR_UNIT_OF_MEASUREMENT)
-        # Exclude states with unsupported unit from statistics
-        if state_unit not in valid_units:
+    if any(unit not in valid_units for unit in all_units):
+        states_by_unit: list[list[tuple[float, State]]] = [
+            list(states)
+            for _, states in itertools.groupby(
+                fstates, key=lambda x: x[1].attributes.get(ATTR_UNIT_OF_MEASUREMENT)
+            )
+        ]
+
+        if SEEN_CHANGED_UNIT not in hass.data:
+            hass.data[SEEN_CHANGED_UNIT] = set()
+
+        if (
+            len(states_by_unit) == 2
+            and state_unit == statistics_unit
+            and entity_id not in hass.data[SEEN_CHANGED_UNIT]
+        ):
+            # Potential unit migration, silently drop states with unexpected units once
+            hass.data[SEEN_CHANGED_UNIT].add(entity_id)
+            fstates = states_by_unit[1]
+        else:
+            # Exclude states with unsupported unit from statistics
             if WARN_UNSUPPORTED_UNIT not in hass.data:
                 hass.data[WARN_UNSUPPORTED_UNIT] = set()
             if entity_id not in hass.data[WARN_UNSUPPORTED_UNIT]:
@@ -363,8 +379,18 @@ def _normalize_states(
                     statistics_unit,
                     LINK_DEV_STATISTICS,
                 )
-            continue
+                fstates = [
+                    (fstate, state)
+                    for fstate, state in fstates
+                    if state.attributes.get(ATTR_UNIT_OF_MEASUREMENT) in valid_units
+                ]
 
+    valid_fstates: list[tuple[float, State]] = []
+    convert: Callable[[float], float] | None = None
+    last_unit: str | None | UndefinedType = UNDEFINED
+
+    for fstate, state in fstates:
+        state_unit = state.attributes.get(ATTR_UNIT_OF_MEASUREMENT)
         if state_unit != last_unit:
             # The unit of measurement has changed since the last state change
             # recreate the converter factory