diff --git a/src/repairwheel/repair.py b/src/repairwheel/repair.py
index 6fb02ff..730e544 100644
--- a/src/repairwheel/repair.py
+++ b/src/repairwheel/repair.py
@@ -1,4 +1,6 @@
 import argparse
+import datetime
+import os
 import shutil
 import sys
 import tempfile
@@ -63,6 +65,15 @@ def main():
     parser = make_parser()
     args = parser.parse_args()
 
+    if "SOURCE_DATE_EPOCH" in os.environ:
+        try:
+            epoch = int(os.environ["SOURCE_DATE_EPOCH"])
+            mtime = datetime.datetime.utcfromtimestamp(epoch)
+        except ValueError:
+            fatal(f"SOURCE_DATE_EPOCH value cannot be parsed as a number: {os.environ['SOURCE_DATE_EPOCH']}")
+    else:
+        mtime = None
+
     original_wheel: Path = args.wheel.resolve()
     out_dir: Path = args.output_dir.resolve()
     lib_path: List[Path] = [lp.resolve() for lp in (args.lib_dir or [])]
@@ -92,7 +103,7 @@ def main():
         patched_wheel = find_written_wheel(temp_wheel_dir)
 
         out_dir.mkdir(parents=True, exist_ok=True)
-        out_wheel = write_canonical_wheel(original_wheel, patched_wheel, out_dir)
+        out_wheel = write_canonical_wheel(original_wheel, patched_wheel, out_dir, mtime=mtime)
 
     print("Wrote", out_wheel)
 
diff --git a/src/repairwheel/wheel.py b/src/repairwheel/wheel.py
index 0ded4c6..ebe3911 100644
--- a/src/repairwheel/wheel.py
+++ b/src/repairwheel/wheel.py
@@ -7,7 +7,7 @@
 from datetime import datetime
 from io import StringIO
 from pathlib import Path
-from typing import BinaryIO, List, Tuple
+from typing import BinaryIO, List, Optional, Tuple
 from zipfile import ZipFile, ZipInfo
 
 from packaging.utils import parse_wheel_filename
@@ -68,7 +68,7 @@ def write_canonical_wheel(
     out_dir: Path,
     default_file_mode: int = 0o664,
     default_dir_mode: int = 0o775,
-    mtime: datetime = DEFAULT_MTIME,
+    mtime: Optional[datetime] = None,
     compression: int = zipfile.ZIP_DEFLATED,
 ) -> Path:
     """This function rewrites a wheel in a canonical form.
@@ -80,6 +80,9 @@ def write_canonical_wheel(
     Because Windows doesn't support posix file modes, we use corresponding modes in the original file if they exist.
     Else we use the default mode.
     """
+    if mtime is None:
+        mtime = DEFAULT_MTIME
+
     out_wheel = out_dir / patched_wheel.name
     dist_name, dist_version, _, _ = parse_wheel_filename(patched_wheel.name)