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Norris, who turns 32 in March, is expected to get the chance to compete for a spot in the rotation. He was 6-10 with a 5.10 ERA in 35 games (19 starts) last season with the Braves and Dodgers.
Norris is 62-78 with a 4.51 ERA in 231 games (185 starts) in eight years with the Astros, Orioles, Padres, Braves and Dodgers.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.