diff --git a/changes/2309.feature.rst b/changes/2309.feature.rst
new file mode 100644
index 000000000..c00f8df2d
--- /dev/null
+++ b/changes/2309.feature.rst
@@ -0,0 +1 @@
+Briefcase now supports license files with names "LICENCE", "LICENSE" and "COPYING" with the extensions ".rst", ".md" and ".txt".
diff --git a/src/briefcase/commands/convert.py b/src/briefcase/commands/convert.py
index 0a61ab8d5..5ddd06257 100644
--- a/src/briefcase/commands/convert.py
+++ b/src/briefcase/commands/convert.py
@@ -664,9 +664,8 @@ def migrate_necessary_files(self, project_dir, test_source_dir, module_name):
         self.merge_or_copy_pyproject(project_dir / "pyproject.toml")
 
         # Copy license file if not already there
-        license_file = self.pep621_data.get("license", {}).get("file")
-
-        if license_file is None and not (self.base_path / "LICENSE").exists():
+        license = find_license_filename()
+        if license is None:
             self.console.warning(
                 f"\nLicense file not found in '{self.base_path}'. "
                 "Briefcase will create a template 'LICENSE' file."
@@ -822,3 +821,27 @@ def find_changelog_filename(base_path):
         if changelog.is_file():
             return format
     return None
+
+
+def find_license_filename(base_path):
+    """Find a valid license file in a given directory.
+
+    :param base_Path: The directory to search
+    :returns: The filename of a license if one is found. Else none if no such
+        license could be found.
+    """
+    # Collect all possible license file formats.
+    license_formats = [
+        f"{name}{extension}"
+        for name in ["LICENSE", "LICENCE", "COPYING"]
+        for extension in ["", ".md", ".rst", ".txt"]
+    ]
+
+    # If a particular format is found, it returns it as the license.
+    for file_format in license_formats:
+        license = base_path / file_format
+        if license.is_file():
+            return file_format
+
+    # Else, no such license exists and return None.
+    return None
diff --git a/src/briefcase/platforms/linux/system.py b/src/briefcase/platforms/linux/system.py
index 3804cc042..81cf56057 100644
--- a/src/briefcase/platforms/linux/system.py
+++ b/src/briefcase/platforms/linux/system.py
@@ -15,7 +15,7 @@
     RunCommand,
     UpdateCommand,
 )
-from briefcase.commands.convert import find_changelog_filename
+from briefcase.commands.convert import find_changelog_filename, find_license_filename
 from briefcase.config import AppConfig, merge_config
 from briefcase.exceptions import BriefcaseCommandError, UnsupportedHostError
 from briefcase.integrations.docker import Docker, DockerAppContext
@@ -736,7 +736,7 @@ def build_app(self, app: AppConfig, **kwargs):
 
         with self.console.wait_bar("Installing license..."):
             if license_file := app.license.get("file"):
-                license_file = self.base_path / license_file
+                license_file = find_license_filename()
                 if license_file.is_file():
                     self.tools.shutil.copy(license_file, doc_folder / "copyright")
                 else:
@@ -764,7 +764,7 @@ def build_app(self, app: AppConfig, **kwargs):
                     """\
 Your project does not contain a LICENSE definition.
 
-Create a file named `LICENSE` in the same directory as your `pyproject.toml`
+Create a file named `LICENSE`, `LICENCE` or `COPYING` in the same directory as your `pyproject.toml`
 with your app's licensing terms, and set `license.file = 'LICENSE'` in your
 app's configuration.
 """
diff --git a/tests/commands/convert/test_find_license_filename.py b/tests/commands/convert/test_find_license_filename.py
new file mode 100644
index 000000000..0888df547
--- /dev/null
+++ b/tests/commands/convert/test_find_license_filename.py
@@ -0,0 +1,42 @@
+import pytest
+
+from briefcase.platforms.linux.system import find_license_filename
+
+from ...utils import create_file
+
+
+def test_no_license(tmp_path):
+    """License file does not exist"""
+    assert find_license_filename(tmp_path) is None
+
+
+def test_no_valid_license(tmp_path):
+    """License file exists but with invalid name format so its not accepted"""
+    license_file = tmp_path / "base_path/invalid_license_format"
+    create_file(license_file, "First App License")
+    assert find_license_filename(tmp_path / "base_path") is None
+
+
+@pytest.mark.parametrize(
+    "license_filename",
+    [
+        f"{name}{extension}"
+        for name in ["LICENSE", "LICENCE", "COPYING"]
+        for extension in ["", ".md", ".rst", ".txt"]
+    ],
+)
+def test_has_license(tmp_path, license_filename):
+    """Makes sure all formats are accepted"""
+    license_file = tmp_path / f"base_path/{license_filename}"
+    create_file(license_file, "First App License")
+    assert find_license_filename(tmp_path / "base_path") == license_filename
+
+
+def test_multiple_changefile(tmp_path):
+    """If there's more than one license, only one is found."""
+
+    license_file1 = tmp_path / "base_path/LICENCE.txt"
+    license_file2 = tmp_path / "base_path/LICENSE.md"
+    create_file(license_file1, "First App License")
+    create_file(license_file2, "First App Licence")
+    assert find_license_filename(tmp_path / "base_path") == "LICENSE.md"