The Cubs designated Norris for assignment Sunday, Jordan Bastian of MLB.com reports.
Norris will cede his spot on the 40-man roster and 26-man active roster to fellow reliever Erich Uelmen, whose contract was selected from Triple-A Iowa. Over his 30 innings with the Cubs this season, Norris turned in a 6.90 ERA and 1.47 WHIP.