Norris signed a minor-league deal with the Guardians on Friday, Mandy Bell of MLB.com reports.
After being released by the Reds on Monday, the 29-year-old reliever will get a shot with Cleveland and report directly to minor-league camp. Norris put up a 5.22 ERA and 1.26 WHIP over 58.2 major-league innings last season with the Cubs and Tigers, and he will likely begin the season at Triple-A.