The 34-year-old was 3-6 with a 3.59 ERA in 57.2 innings out of the bullpen with the St. Louis Cardinals last year. He had 67 strikeouts and 21 walks.
In his 10-season career, Norris is 67-90 with a 4.45 ERA. The native of Greenbrae, Calif., primarily has been a reliever the past two years after beginning his career as a starter.
Norris also has spent time with the Houston Astros, Baltimore Orioles and Los Angeles Angels.