The deal, agreed to in mid-December, was announced by the Red Sox on Wednesday.
Breslow was acquired from Arizona late in the 2012 season. The 34-year-old has pitched in 120 games for the Red Sox during the past two years, including 60 in 2014 after starting the season on the disabled list. He finished last season with a 5.96 ERA, 37 strikeouts and 28 walks.
Breslow made his big league debut in 2005 with San Diego and also has played for Cleveland, Minnesota and Oakland.
Catcher Dan Butler was designated for assignment to make room for Breslow on the 40-man roster.