Martin was 1-1 with a 4.08 ERA in 20 games with the Braves. He had 22 strikeouts and one walk in 17⅔ innings.
Martin will earn $7 million in each year of the deal and agreed to a provision to donate $70,000 annually to charity. His signing comes on the same day the Braves introduced left-hander Will Smith, who agreed to a $40 million, three-year contract.
The 6-foot-8 Martin has a 4.51 ERA in his big league career in 144 games, all in relief, with Colorado, the New York Yankees, Texas and Atlanta.