New York had declined a $1.25 million option on the right-hander, who was not on the Yankees' postseason roster.
Mitre, who turns 29 next month, had elbow ligament replacement surgery in July 2008 and agreed to a minor league contract with the Yankees last offseason. He sat out the first 50 games while serving a suspension for testing positive for a banned substance.
Mitre joined the Yankees in late July and went 3-3 with a 6.79 ERA in nine starts and three relief appearances.
Right-hander Chad Gaudin and left-hander Boone Logan remain eligible for arbitration. Logan was acquired last month from Atlanta along with right-hander Javier Vazquez in the trade that sent outfielder Melky Cabrera to the Braves.