The 25-year-old Ryu appeared in one game for Tampa Bay last season, throwing 1 1/3 shutout innings. He made five starts for Triple-A Durham, going 1-2 with a 4.38 ERA.
Ryu, a native of South Korea, saw his season end early after having arthroscopic surgery on his right elbow in July.
Ryu has appeared in 28 Major League games over the past three seasons, posting a 1-3 record with a 7.49 ERA over 39 2/3 innings with the Chicago Cubs (2006) and Rays (2007-08).
Over parts of seven Minor League seasons in the Cubs organization, Ryu was 42-34 with a 3.52 ERA.
Corey Brock is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.