diff --git a/doc/pyproject_toml.rst b/doc/pyproject_toml.rst
index 9d4f9da1..f8ef6613 100644
--- a/doc/pyproject_toml.rst
+++ b/doc/pyproject_toml.rst
@@ -98,6 +98,8 @@ requires-python
 license
   A table with either a ``file`` key (a relative path to a license file) or a
   ``text`` key (the license text).
+license-files
+  A list of glob patterns for license files to include. Defaults to ``['COPYING*', 'LICENSE*']``.
 authors
   A list of tables with ``name`` and ``email`` keys (both optional) describing
   the authors of the project.
diff --git a/flit_core/flit_core/common.py b/flit_core/flit_core/common.py
index 5385c9c0..719e1072 100644
--- a/flit_core/flit_core/common.py
+++ b/flit_core/flit_core/common.py
@@ -354,6 +354,7 @@ class Metadata(object):
     obsoletes_dist = ()
     requires_external = ()
     provides_extra = ()
+    license_files = ()
     dynamic = ()
 
     metadata_version = "2.3"
@@ -425,6 +426,10 @@ def write_metadata_file(self, fp):
         for clsfr in self.classifiers:
             fp.write(u'Classifier: {}\n'.format(clsfr))
 
+        # TODO: License-File requires Metadata-Version '2.4'
+        # for file in self.license_files:
+        #     fp.write(u'License-File: {}\n'.format(file))
+
         for req in self.requires_dist:
             normalised_req = self._normalise_requires_dist(req)
             fp.write(u'Requires-Dist: {}\n'.format(normalised_req))
diff --git a/flit_core/flit_core/config.py b/flit_core/flit_core/config.py
index 25ad55d0..adf3b3a3 100644
--- a/flit_core/flit_core/config.py
+++ b/flit_core/flit_core/config.py
@@ -60,6 +60,7 @@ class ConfigError(ValueError):
     'readme',
     'requires-python',
     'license',
+    'license-files',
     'authors',
     'maintainers',
     'keywords',
@@ -73,6 +74,8 @@ class ConfigError(ValueError):
     'dynamic',
 }
 
+default_license_files_globs = ['COPYING*', 'LICENSE*']
+
 
 def read_flit_config(path):
     """Read and check the `pyproject.toml` file with data about the package.
@@ -427,6 +430,13 @@ def _prep_metadata(md_sect, path):
     # For internal use, record the main requirements as a '.none' extra.
     res.reqs_by_extra['.none'] = reqs_noextra
 
+    if path:
+        license_files = _license_files_from_globs(
+            path.parent, default_license_files_globs, use_defaults=True
+        )
+        res.referenced_files.extend(license_files)
+        md_dict['license_files'] = license_files
+
     return res
 
 def _expand_requires_extra(re):
@@ -439,6 +449,41 @@ def _expand_requires_extra(re):
                 yield '{} ; extra == "{}"'.format(req, extra)
 
 
+def _license_files_from_globs(project_dir: Path, globs: list[str], use_defaults: bool = False) -> list[str]:
+    license_files: list[Path] = []
+    for pattern in globs:
+        if pattern.startswith("/"):
+            raise ConfigError(
+                "Invalid glob pattern for [project.license-files]: '{}'. "
+                "Pattern must not start with '/'.".format(pattern)
+            )
+        if ".." in pattern:
+            raise ConfigError(
+                "Invalid glob pattern for [project.license-files]: '{}'. "
+                "Pattern must not contain '..'".format(pattern)
+            )
+        try:
+            files = list(
+                filter(
+                    lambda file: file.is_file(),
+                    map(
+                        lambda file: file.relative_to(project_dir),
+                        project_dir.glob(pattern)
+                    )
+                )
+            )
+        except ValueError as ex:
+            raise ConfigError(
+                "Invalid glob pattern for [project.license-files]: '{}'. {}".format(pattern, ex.args[0])
+            )
+
+        if not files and not use_defaults:
+            raise ConfigError(
+                "No files found for [project.license-files]: '{}' pattern".format(pattern)
+            )
+        license_files.extend(files)
+    return sorted(map(str, license_files))
+
 def _check_type(d, field_name, cls):
     if not isinstance(d[field_name], cls):
         raise ConfigError(
@@ -551,6 +596,18 @@ def read_pep621_metadata(proj, path) -> LoadedConfig:
                 "file or text field required in [project.license] table"
             )
 
+    license_files = []
+    if 'license-files' in proj:
+        _check_type(proj, 'license-files', list)
+        globs = proj['license-files']
+        license_files = _license_files_from_globs(path.parent, globs)
+    else:
+        license_files = _license_files_from_globs(
+            path.parent, default_license_files_globs, use_defaults=True
+        )
+    lc.referenced_files.extend(license_files)
+    md_dict['license_files'] = license_files
+
     if 'authors' in proj:
         _check_type(proj, 'authors', list)
         md_dict.update(pep621_people(proj['authors']))
diff --git a/flit_core/flit_core/wheel.py b/flit_core/flit_core/wheel.py
index 66b0ac29..1a4a30c9 100644
--- a/flit_core/flit_core/wheel.py
+++ b/flit_core/flit_core/wheel.py
@@ -183,10 +183,8 @@ def write_metadata(self):
             with self._write_to_zip(self.dist_info + '/entry_points.txt') as f:
                 common.write_entry_points(self.entrypoints, f)
 
-        for base in ('COPYING', 'LICENSE'):
-            for path in sorted(self.directory.glob(base + '*')):
-                if path.is_file():
-                    self._add_file(path, '%s/%s' % (self.dist_info, path.name))
+        for file in self.metadata.license_files:
+            self._add_file(self.directory / file, '%s/licenses/%s' % (self.dist_info, file))
 
         with self._write_to_zip(self.dist_info + '/WHEEL') as f:
             _write_wheel_file(f, supports_py2=self.metadata.supports_py2)
diff --git a/flit_core/pyproject.toml b/flit_core/pyproject.toml
index a027ff0c..5c12d6f2 100644
--- a/flit_core/pyproject.toml
+++ b/flit_core/pyproject.toml
@@ -13,6 +13,7 @@ dependencies = []
 requires-python = '>=3.6'
 readme = "README.rst"
 license = {file = "LICENSE"}
+license-files = ["LICENSE*", "flit_core/vendor/**/LICENSE*"]
 classifiers = [
     "License :: OSI Approved :: BSD License",
     "Topic :: Software Development :: Libraries :: Python Modules",
diff --git a/flit_core/tests_core/samples/pep621_license_files/LICENSE b/flit_core/tests_core/samples/pep621_license_files/LICENSE
new file mode 100644
index 00000000..7f5c1948
--- /dev/null
+++ b/flit_core/tests_core/samples/pep621_license_files/LICENSE
@@ -0,0 +1 @@
+This file should be added to wheels
diff --git a/flit_core/tests_core/samples/pep621_license_files/README.rst b/flit_core/tests_core/samples/pep621_license_files/README.rst
new file mode 100644
index 00000000..304360ca
--- /dev/null
+++ b/flit_core/tests_core/samples/pep621_license_files/README.rst
@@ -0,0 +1 @@
+Readme
diff --git a/flit_core/tests_core/samples/pep621_license_files/module/vendor/LICENSE_VENDOR b/flit_core/tests_core/samples/pep621_license_files/module/vendor/LICENSE_VENDOR
new file mode 100644
index 00000000..7f5c1948
--- /dev/null
+++ b/flit_core/tests_core/samples/pep621_license_files/module/vendor/LICENSE_VENDOR
@@ -0,0 +1 @@
+This file should be added to wheels
diff --git a/flit_core/tests_core/samples/pep621_license_files/module1a.py b/flit_core/tests_core/samples/pep621_license_files/module1a.py
new file mode 100644
index 00000000..87f0370d
--- /dev/null
+++ b/flit_core/tests_core/samples/pep621_license_files/module1a.py
@@ -0,0 +1,3 @@
+"""Example module"""
+
+__version__ = '0.1'
diff --git a/flit_core/tests_core/samples/pep621_license_files/pyproject.toml b/flit_core/tests_core/samples/pep621_license_files/pyproject.toml
new file mode 100644
index 00000000..1882615a
--- /dev/null
+++ b/flit_core/tests_core/samples/pep621_license_files/pyproject.toml
@@ -0,0 +1,39 @@
+[build-system]
+requires = ["flit_core >=3.2,<4"]
+build-backend = "flit_core.buildapi"
+
+[project]
+name = "module1"
+authors = [
+    {name = "Sir Röbin", email = "robin@camelot.uk"}
+]
+maintainers = [
+    {name = "Sir Galahad"}
+]
+readme = "README.rst"
+license-files = ["**/LICENSE*"]
+requires-python = ">=3.7"
+dependencies = [
+    "requests >= 2.18",
+    "docutils",
+]
+keywords = ["example", "test"]
+dynamic = [
+    "version",
+    "description",
+]
+
+[project.optional-dependencies]
+test = [
+  "pytest",
+  "mock; python_version<'3.6'"
+]
+
+[project.urls]
+homepage = "http://github.com/sirrobin/module1"
+
+[project.entry-points.flit_test_example]
+foo = "module1:main"
+
+[tool.flit.module]
+name = "module1a"
diff --git a/flit_core/tests_core/test_config.py b/flit_core/tests_core/test_config.py
index 7d9e2c86..4586db5e 100644
--- a/flit_core/tests_core/test_config.py
+++ b/flit_core/tests_core/test_config.py
@@ -1,5 +1,8 @@
 import logging
+import re
+import os
 from pathlib import Path
+from unittest.mock import patch
 import pytest
 
 from flit_core import config
@@ -178,3 +181,38 @@ def test_bad_pep621_readme(readme, err_match):
     }
     with pytest.raises(config.ConfigError, match=err_match):
         config.read_pep621_metadata(proj, samples_dir / 'pep621')
+
+
+@pytest.mark.parametrize(('value', 'files'), [
+    ('[]', []),
+    ('["LICENSE"]', ["LICENSE"]),
+    ('["LICENSE*"]', ["LICENSE"]),
+    ('["**/LICENSE*"]', ["LICENSE", "module/vendor/LICENSE_VENDOR"]),
+    ('["module/vendor/LICENSE*"]', ["module/vendor/LICENSE_VENDOR"]),
+    ('["LICENSE", "module/**/LICENSE*"]', ["LICENSE", "module/vendor/LICENSE_VENDOR"]),
+])
+def test_pep621_license_files(value, files):
+    path = samples_dir / 'pep621_license_files' / 'pyproject.toml'
+    data = path.read_text()
+    data = re.sub(r"(^license-files = )(?:\[.*\])", r"\g<1>{}".format(value), data, 1, flags=re.M)
+    dir = os.getcwd()
+    try:
+        os.chdir(samples_dir / 'pep621_license_files')
+        with patch("pathlib.Path.read_text", return_value=data):
+            info = config.read_flit_config(path)
+            assert info.metadata['license_files'] == files
+    finally:
+        os.chdir(dir)
+
+
+@pytest.mark.parametrize(('proj_bad', 'err_match'), [
+    ({'license-files': ["/LICENSE"]}, "'/LICENSE'.+must not start with '/'"),
+    ({'license-files': ["../LICENSE"]}, "'../LICENSE'.+must not contain '..'"),
+    ({'license-files': ["**LICENSE"]}, "'\\*\\*LICENSE'.+Invalid pattern"),
+    ({'license-files': ["NOT_FOUND"]}, "No files found.+'NOT_FOUND'"),
+])
+def test_bad_pep621_license_files(proj_bad, err_match):
+    proj = {'name': 'module1', 'version': '1.0', 'description': 'x'}
+    proj.update(proj_bad)
+    with pytest.raises(config.ConfigError, match=err_match):
+        config.read_pep621_metadata(proj, samples_dir / 'pep621')
diff --git a/flit_core/tests_core/test_wheel.py b/flit_core/tests_core/test_wheel.py
index 310f9c6c..b0a9f0a3 100644
--- a/flit_core/tests_core/test_wheel.py
+++ b/flit_core/tests_core/test_wheel.py
@@ -1,3 +1,4 @@
+import os
 from pathlib import Path
 from zipfile import ZipFile
 
@@ -45,3 +46,16 @@ def test_data_dir(tmp_path):
     assert_isfile(info.file)
     with ZipFile(info.file, 'r') as zf:
         assert 'module1-0.1.data/data/share/man/man1/foo.1' in zf.namelist()
+
+
+def test_license_files(tmp_path):
+    dir = os.getcwd()
+    try:
+        os.chdir(samples_dir / 'pep621_license_files')
+        info = make_wheel_in(samples_dir / 'pep621_license_files' / 'pyproject.toml', tmp_path)
+        assert_isfile(info.file)
+        with ZipFile(info.file, 'r') as zf:
+            assert 'module1-0.1.dist-info/licenses/LICENSE' in zf.namelist()
+            assert 'module1-0.1.dist-info/licenses/module/vendor/LICENSE_VENDOR' in zf.namelist()
+    finally:
+        os.chdir(dir)
diff --git a/tests/test_wheel.py b/tests/test_wheel.py
index e39a2b0e..431c9b48 100644
--- a/tests/test_wheel.py
+++ b/tests/test_wheel.py
@@ -90,7 +90,7 @@ def test_wheel_src_module(copy_sample):
     with unpack(whl_file) as unpacked:
         assert_isfile(Path(unpacked, 'module3.py'))
         assert_isdir(Path(unpacked, 'module3-0.1.dist-info'))
-        assert_isfile(Path(unpacked, 'module3-0.1.dist-info', 'LICENSE'))
+        assert_isfile(Path(unpacked, 'module3-0.1.dist-info', 'licenses', 'LICENSE'))
 
 def test_editable_wheel_src_module(copy_sample):
     td = copy_sample('module3')