Breslow, who had been eligible for salary arbitration, agreed to a two-year contract, with a club option for 2015.
In 63 combined appearances between Arizona and Boston last season, Breslow, 32, went 3-0 with a 2.70 ERA. He was acquired by the Red Sox on July 31 from the Diamondbacks in exchange for pitcher Matt Albers and outfielder Scott Podsednik.
Breslow, a native of New Haven, Conn., and a Yale graduate, has made 60 or more appearances in each of the last four seasons for a total of 282. That ranks fourth among all major league relievers since 2009.
Originally selected by the Milwaukee Brewers in the 26th round of the 2002 June draft, Breslow has a 15-17 record with a 3.00 ERA in 358 career games. In Boston, he is 1-2 with a 3.09 ERA in 36 appearances.