A seven-year veteran, Wright also has spent time with the Astros and Rays. He enters his age-30 season with a 3.25 ERA over 166 1/3 innings since 2011, with 8.5 strikeouts per nine innings and 3.2 walks per nine innings. Lefties have hit only .238/.315/.331 against Wright in his career.
Along with Wright, Baltimore will potentially have four southpaws in its bullpen, with closer Zach Britton joined by Brian Matusz and T.J. McFarland.
With the Wright signing, Baltimore's 40-man roster is full.
Andrew Simon is a reporter for MLB.com. Follow him on Twitter @AndrewSimonMLB. This story was not subject to the approval of Major League Baseball or its clubs.