diff --git a/dev/release/add_backports.py b/dev/release/add_backports.py
index 78bcf7879b..d36086b95c 100644
--- a/dev/release/add_backports.py
+++ b/dev/release/add_backports.py
@@ -7,6 +7,7 @@
     add_backports_to_body,
     add_rc_task_to_body,
     add_sync_changelog_task_to_body,
+    is_release_complete,
     load_release_tracking_template,
     parse_checklist_state,
 )
@@ -33,16 +34,31 @@ def run(self) -> int:
             )
             try:
                 open_issues = self.gh.get_open_tracking_issues()
-                if len(open_issues) > 1:
+                # An open issue whose release has already been tagged is
+                # finished; it just hasn't been closed. Don't add work to it.
+                active_issues = []
+                for issue in open_issues:
+                    body = self.gh.get_issue_body(issue["number"])
+                    if is_release_complete(body):
+                        print(
+                            "::warning::Ignoring open release tracking issue"
+                            f" #{issue['number']} ({issue['title']}): its"
+                            " 'Tag Final' task is done, so the release is"
+                            " complete. Consider closing it."
+                        )
+                        continue
+                    active_issues.append(issue)
+
+                if len(active_issues) > 1:
                     print(
                         "::error::Multiple open release tracking issues found."
                         " Cannot determine active one:"
                     )
-                    for issue in open_issues:
+                    for issue in active_issues:
                         print(f"- #{issue['number']}: {issue['title']}")
                     return 1
-                elif len(open_issues) == 1:
-                    issue_num = open_issues[0]["number"]
+                elif len(active_issues) == 1:
+                    issue_num = active_issues[0]["number"]
                     print(
                         f"Auto-discovered active release tracking issue: #{issue_num}"
                     )
diff --git a/dev/release/release_issue.py b/dev/release/release_issue.py
index 6bfa0f58e0..1b71e4a082 100644
--- a/dev/release/release_issue.py
+++ b/dev/release/release_issue.py
@@ -280,6 +280,25 @@ def parse_checklist_state(body):
     return state
 
 
+def is_release_complete(body: str) -> bool:
+    """Returns whether the release tracked by an issue body has been completed.
+
+    A release is complete once its "Tag Final" task is done: the checklist
+    item is checked, or it carries `status=done` metadata (as written by the
+    promote step). An open tracking issue in this state should not receive
+    further work, such as new backports.
+
+    Args:
+        body: The release tracking issue body.
+
+    Returns:
+        True if the "Tag Final" task is done, False otherwise (including when
+        the task is absent).
+    """
+    tag_final = parse_checklist_state(body)["tag_final"]
+    return tag_final.checked or tag_final.status == "done"
+
+
 def parse_backports(body):
     """Parses the ## Backports checklist section."""
     body = body.replace("\r\n", "\n")
diff --git a/tests/tools/private/release/add_backports_test.py b/tests/tools/private/release/add_backports_test.py
index 08fd9a888f..24636c6e3c 100644
--- a/tests/tools/private/release/add_backports_test.py
+++ b/tests/tools/private/release/add_backports_test.py
@@ -77,6 +77,84 @@ def test_add_backports_auto_discover_no_issues_creates_patch_release(
     assert "- [ ] Tag Final" in body
 
 
+def test_add_backports_auto_discover_skips_complete_release_creates_patch_release(
+    mock_gh, mock_git, release_tool_env
+):
+    # 1.2.1 has already been tagged (Tag Final done) but the issue was never
+    # closed. It must be left alone and a new 1.2.2 issue created instead.
+    mock_git.get_tags.return_value = ["1.2.0", "1.2.1"]
+    mock_git.get_current_branch.return_value = "main"
+    complete_body = """
+## Checklist
+- [x] Sync Changelog #100 | status=done
+- [x] Tag Final | status=done tag=1.2.1 commit= abcdef12
+
+## Backports
+- [x] #100 | status=done
+"""
+    complete_issue_num = mock_gh.create_issue(
+        title="Release 1.2.1",
+        body=complete_body,
+        labels=["type: release"],
+    )
+
+    args = argparse.Namespace(issue=None, prs=["124"])
+
+    result = AddBackports(args, mock_gh, mock_git).run()
+
+    assert result == 0
+    # The completed issue is untouched.
+    assert mock_gh.get_issue_body(complete_issue_num) == complete_body
+
+    open_issues = mock_gh.get_open_tracking_issues()
+    assert len(open_issues) == 2
+    new_issue = next(i for i in open_issues if i["number"] != complete_issue_num)
+    assert new_issue["title"] == "Release 1.2.2"
+    body = new_issue["body"]
+    assert "- [ ] #124" in body
+    assert "- [ ] Sync Changelog #124" in body
+    assert "- [ ] Tag Final" in body
+
+
+def test_add_backports_auto_discover_ignores_complete_release_among_multiple(
+    mock_gh,
+):
+    # A stale-but-complete issue alongside an active one should not cause the
+    # "multiple open issues" error; the active one is used.
+    complete_issue_num = mock_gh.create_issue(
+        title="Release 1.2.1",
+        body="""
+## Checklist
+- [x] Tag Final | status=done tag=1.2.1 commit= abcdef12
+
+## Backports
+""",
+        labels=["type: release"],
+    )
+    active_issue_num = mock_gh.create_issue(
+        title="Release 1.3.0",
+        body="""
+## Checklist
+- [ ] Prepare Release
+- [ ] Create Release branch
+- [ ] Tag Final
+
+## Backports
+""",
+        labels=["type: release"],
+    )
+
+    args = argparse.Namespace(issue=None, prs=["124"])
+
+    result = AddBackports(args, mock_gh).run()
+
+    assert result == 0
+    assert "#124" not in mock_gh.get_issue_body(complete_issue_num)
+    active_body = mock_gh.get_issue_body(active_issue_num)
+    assert "- [ ] #124" in active_body
+    assert "- [ ] Sync Changelog #124" in active_body
+
+
 def test_add_backports_patch_release_no_rc_added(mock_gh):
     args = argparse.Namespace(issue=123, prs=["124"])
     mock_gh.issues[123] = {
diff --git a/tests/tools/private/release/release_issue_test.py b/tests/tools/private/release/release_issue_test.py
index 3530dfd38a..be1f2a8c40 100644
--- a/tests/tools/private/release/release_issue_test.py
+++ b/tests/tools/private/release/release_issue_test.py
@@ -2,6 +2,7 @@
     add_backports_to_body,
     add_sync_changelog_task_to_body,
     format_metadata_line,
+    is_release_complete,
     load_release_tracking_template,
     parse_backports,
     parse_checklist_state,
@@ -194,6 +195,22 @@ def test_parse_checklist_state_with_sync_changelogs():
     assert task_126.pr is None
 
 
+def test_is_release_complete():
+    assert not is_release_complete("- [ ] Tag Final")
+    assert is_release_complete("- [x] Tag Final")
+    assert is_release_complete(
+        "- [x] Tag Final | status=done tag=2.0.0 commit= abcdef12"
+    )
+    # status=done is authoritative even if the box is somehow unchecked.
+    assert is_release_complete("- [ ] Tag Final | status=done tag=2.0.0")
+    # A failed promote attempt leaves the release incomplete.
+    assert not is_release_complete(
+        "- [ ] Tag Final | status=error-rc-tag-not-branch-head rc=2.0.0rc1"
+    )
+    # No Tag Final task at all (e.g. malformed body) is not complete.
+    assert not is_release_complete("## Checklist\n- [x] Prepare Release\n")
+
+
 def test_load_release_tracking_template(tmp_path):
     template_file = tmp_path / "template.md"
     template_file.write_text("""## Checklist