New York last week declined a $6 million option on the 33-year-old reliever, choosing to pay a $250,000 buyout.
Marte was acquired with outfielder Xavier Nady from Pittsburgh on July 26 for pitchers Ross Ohlendorf, Jeff Karstens and Daniel McCutchen and outfielder Jose Tabata. Marte went 1-3 with a 5.40 ERA in 25 games for the Yankees and 5-3 with a 4.02 ERA overall.
"Early in the year we asked him probably to do more than he physically was capable of doing," New York manager Joe Girardi said Thursday. "We signed him to three-year deal because we wanted to keep him more than a year and, obviously, he would have been available on the free-agent market after the 2009 season."
Marte gets $3.75 million next year and $4 million in each of the following two seasons under the agreement announced Wednesday. The Yankees have a $4 million option for 2012 with a $250,000 buyout.
Rookie Phil Coke joined Marte in the bullpen last September and looked impressive, giving the Yankees two lefty relievers.
"It really set up our bullpen nice," Girardi said. "Damaso has late-inning experience. He's done a lot of that in his career. And he's tough on left-handed hitters. He's the type of guy that it's hard to get a good look at off of him because he kinds of slings it from behind left-handed hitters."
New York also finalized its coaching changes that general manager Brian Cashman said were likely last week. Mick Kelleher, who had been minor league defensive coordinator, becomes first base coach. Tony Pena switches from first base to bench coach, and Rob Thomson move from bench coach to third base to replace Bobby Meacham, fired last month after one season.