Kirkman was out of options. He was 2-5 with a 5.17 ERA in 82 career appearances with the Rangers over the past four years. He had a 5.25 ERA this spring.
The Rangers also announced that pitcher Scott Baker has passed his physical and will join the rotation at Triple-A Round Rock.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.