The deal is worth $2.5 million, $500,000 less than what sources said the Arizona Diamondbacks offered the right-hander Wednesday.
Chamberlain had spent his entire seven-year career with the Yankees. He exploded on the scene as a 21-year-old in 2007. In 19 games, he posted a 0.38 ERA with 34 strikeouts in 24 relief innings.
The Yankees then tried to turn him into a starter. In 42 games and 12 starts the next season, he posted a 4-3 record and a 2.60 ERA, again with more strikeouts than innings pitched.
But things went downhill from there. Injuries and ineffectiveness ended the starter experiment, and Chamberlain never really developed into a reliable bridge to Hall of Fame closer Mariano Rivera.
Last season, Chamberlain appeared in 45 games and posted a 4.93 ERA and 1.74 WHIP.
"Obviously, Joba didn't have what we or he expected this past season, so there's probably a good chance for a rebound season for him," said Yankees general manager Brian Cashman.
Tigers general manager Dave Dombrowski had recently indicated that he would look for bullpen help. Last year's closer, Joaquin Benoit, was replaced by Joe Nathan. Bruce Rondon appears slotted for a setup role.