The deal is worth $18 million, according to a league source.
The 39-year-old right-handed closer saved 26 games in 2014 for the Red Sox and posted a 6-5 record and 2.52 ERA in his second season with the team. He had a career-best 1.09 ERA, going 4-1 with 21 saves in 2013 for the Red Sox.
He was brilliant during the 2013 postseason, saving 7 games and allowing 1 earned run in 13 2/3 innings as the Red Sox went on to win the World Series. He was the named the MVP of the American League Championship Series after he went 1-0 with three saves in Boston's series victory over the Detroit Tigers.
ESPNBoston's Gordon Edes contributed to this report.