General manager Josh Byrnes says Owings is a "proven contributor" as a starter and a reliever. The deal was announced Thursday.
Owings was 8-0 with a career-best 3.57 ERA in 33 games, including four starts, for the Arizona Diamondbacks in 2011. The Diamondbacks didn't tender him a contract after last season.
He made his big league debut with the Diamondbacks in 2007, when Byrnes was Arizona's GM.
Owings can also be used as a pinch hitter. He is a .286 (58 for 203) career hitter, with nine home runs and 35 RBIs. He has a career .297 (47 for 158) average as a pitcher, tops among all pitchers with 100-or-more at-bats since 2007.