diff --git a/CHANGELOG.md b/CHANGELOG.md
index f129a59d70..9acada7d98 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
 
 ## Unreleased
 
+
 ### Fixed
 
 - Fixed `Pilot.click` not working with `times` parameter https://github.com/Textualize/textual/pull/5398
@@ -18,6 +19,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
 ### Changed
 
 - The content of an `Input` will now only be automatically selected when the widget is focused by the user, not when the app itself has regained focus (similar to web browsers). https://github.com/Textualize/textual/pull/5379
+- Updated `TextArea` and `Input` behavior when there is a selection and the user presses left or right https://github.com/Textualize/textual/pull/5400
 
 
 ## [1.0.0] - 2024-12-12
diff --git a/src/textual/widgets/_input.py b/src/textual/widgets/_input.py
index 78e501ffe4..463f9e13c8 100644
--- a/src/textual/widgets/_input.py
+++ b/src/textual/widgets/_input.py
@@ -761,11 +761,14 @@ def action_cursor_left(self, select: bool = False) -> None:
         Args:
             select: If `True`, select the text to the left of the cursor.
         """
+        start, end = self.selection
         if select:
-            start, end = self.selection
             self.selection = Selection(start, end - 1)
         else:
-            self.cursor_position -= 1
+            if self.selection.is_empty:
+                self.cursor_position -= 1
+            else:
+                self.cursor_position = min(start, end)
 
     def action_cursor_right(self, select: bool = False) -> None:
         """Accept an auto-completion or move the cursor one position to the right.
@@ -773,15 +776,18 @@ def action_cursor_right(self, select: bool = False) -> None:
         Args:
             select: If `True`, select the text to the right of the cursor.
         """
+        start, end = self.selection
         if select:
-            start, end = self.selection
             self.selection = Selection(start, end + 1)
         else:
             if self._cursor_at_end and self._suggestion:
                 self.value = self._suggestion
                 self.cursor_position = len(self.value)
             else:
-                self.cursor_position += 1
+                if self.selection.is_empty:
+                    self.cursor_position += 1
+                else:
+                    self.cursor_position = max(start, end)
 
     def action_home(self, select: bool = False) -> None:
         """Move the cursor to the start of the input.
diff --git a/src/textual/widgets/_text_area.py b/src/textual/widgets/_text_area.py
index b011d8d8ae..687ef8107d 100644
--- a/src/textual/widgets/_text_area.py
+++ b/src/textual/widgets/_text_area.py
@@ -1835,10 +1835,16 @@ def action_cursor_left(self, select: bool = False) -> None:
         If the cursor is at the left edge of the document, try to move it to
         the end of the previous line.
 
+        If text is selected, move the cursor to the start of the selection.
+
         Args:
             select: If True, select the text while moving.
         """
-        target = self.get_cursor_left_location()
+        target = (
+            self.get_cursor_left_location()
+            if select or self.selection.is_empty
+            else min(*self.selection)
+        )
         self.move_cursor(target, select=select)
 
     def get_cursor_left_location(self) -> Location:
@@ -1854,10 +1860,16 @@ def action_cursor_right(self, select: bool = False) -> None:
 
         If the cursor is at the end of a line, attempt to go to the start of the next line.
 
+        If text is selected, move the cursor to the end of the selection.
+
         Args:
             select: If True, select the text while moving.
         """
-        target = self.get_cursor_right_location()
+        target = (
+            self.get_cursor_right_location()
+            if select or self.selection.is_empty
+            else max(*self.selection)
+        )
         self.move_cursor(target, select=select)
 
     def get_cursor_right_location(self) -> Location:
diff --git a/tests/input/test_input_terminal_cursor.py b/tests/input/test_input_terminal_cursor.py
index b956a29846..31f1770181 100644
--- a/tests/input/test_input_terminal_cursor.py
+++ b/tests/input/test_input_terminal_cursor.py
@@ -8,7 +8,9 @@ class InputApp(App):
     CSS = "Input { padding: 4 8 }"
 
     def compose(self) -> ComposeResult:
-        yield Input("こんにちは!")
+        # We don't want to select the text on focus, as selected text
+        # has different interactions with the cursor_left action.
+        yield Input("こんにちは!", select_on_focus=False)
 
 
 async def test_initial_terminal_cursor_position():