diff --git a/py-polars/polars/dataframe/frame.py b/py-polars/polars/dataframe/frame.py
index da79a0cf57df..d1f39c3b135a 100644
--- a/py-polars/polars/dataframe/frame.py
+++ b/py-polars/polars/dataframe/frame.py
@@ -4525,7 +4525,7 @@ def rename(
         """
         return self.lazy().rename(mapping, strict=strict).collect(_eager=True)
 
-    def insert_column(self, index: int, column: Series) -> DataFrame:
+    def insert_column(self, index: int, column: IntoExprColumn) -> DataFrame:
         """
         Insert a Series at a certain column index.
 
@@ -4536,7 +4536,7 @@ def insert_column(self, index: int, column: Series) -> DataFrame:
         index
             Index at which to insert the new `Series` column.
         column
-            `Series` to insert.
+            `Series` or expression to insert.
 
         Examples
         --------
@@ -4575,9 +4575,27 @@ def insert_column(self, index: int, column: Series) -> DataFrame:
         │ 4   ┆ 13.0 ┆ true  ┆ 0.0  │
         └─────┴──────┴───────┴──────┘
         """
-        if index < 0:
+        if (original_index := index) < 0:
             index = len(self.columns) + index
-        self._df.insert_column(index, column._s)
+            if index < 0:
+                msg = f"column index {original_index} is out of range (frame has {len(self.columns)} columns)"
+                raise IndexError(msg)
+        elif index > len(self.columns):
+            msg = f"column index {original_index} is out of range (frame has {len(self.columns)} columns)"
+            raise IndexError(msg)
+
+        if isinstance(column, pl.Series):
+            self._df.insert_column(index, column._s)
+        else:
+            if isinstance(column, str):
+                column = F.col(column)
+            if isinstance(column, pl.Expr):
+                cols = self.columns
+                cols.insert(index, column)  # type: ignore[arg-type]
+                self._df = self.select(cols)._df
+            else:
+                msg = f"column must be a Series or Expr, got {column!r} (type={type(column)})"
+                raise TypeError(msg)
         return self
 
     def filter(
diff --git a/py-polars/tests/unit/dataframe/test_df.py b/py-polars/tests/unit/dataframe/test_df.py
index 2389bef36c88..015b64ce6303 100644
--- a/py-polars/tests/unit/dataframe/test_df.py
+++ b/py-polars/tests/unit/dataframe/test_df.py
@@ -458,6 +458,7 @@ def test_assignment() -> None:
 
 
 def test_insert_column() -> None:
+    # insert series
     df = (
         pl.DataFrame({"z": [3, 4, 5]})
         .insert_column(0, pl.Series("x", [1, 2, 3]))
@@ -466,6 +467,39 @@ def test_insert_column() -> None:
     expected_df = pl.DataFrame({"x": [1, 2, 3], "y": [2, 3, 4], "z": [3, 4, 5]})
     assert_frame_equal(expected_df, df)
 
+    # insert expressions
+    df = pl.DataFrame(
+        {
+            "id": ["xx", "yy", "zz"],
+            "v1": [5, 4, 6],
+            "v2": [7, 3, 3],
+        }
+    )
+    df.insert_column(3, (pl.col("v1") * pl.col("v2")).alias("v3"))
+    df.insert_column(1, (pl.col("v2") - pl.col("v1")).alias("v0"))
+
+    expected = pl.DataFrame(
+        {
+            "id": ["xx", "yy", "zz"],
+            "v0": [2, -1, -3],
+            "v1": [5, 4, 6],
+            "v2": [7, 3, 3],
+            "v3": [35, 12, 18],
+        }
+    )
+    assert_frame_equal(df, expected)
+
+    # check that we raise suitable index errors
+    for idx, column in (
+        (10, pl.col("v1").sqrt().alias("v1_sqrt")),
+        (-10, pl.Series("foo", [1, 2, 3])),
+    ):
+        with pytest.raises(
+            IndexError,
+            match=rf"column index {idx} is out of range \(frame has 5 columns\)",
+        ):
+            df.insert_column(idx, column)
+
 
 def test_replace_column() -> None:
     df = (