Cobb, 30, went 12-10 with a 3.66 ERA and 128/44 strikeout-to-walk ratio across 179 1/3 innings (29 starts) last season for Tampa Bay -- his first full year since undergoing Tommy John surgery.
He has allowed 2.6 walks per nine innings throughout his six-year career, and the Orioles surrendered the second-most walks in the American League last season.
Cobb is familiar with the AL East, and has found some success against the division's top teams at their home stadiums. He owns a 5-1 record with a 3.15 ERA in seven starts at Fenway Park and is 1-2 with a 3.12 ERA in five starts at Yankee Stadium.
Cobb earned $4.2 million last season with the Rays.
-- Nick Ostiller