By reaching a deal, the two sides have avoided arbitration.
The Red Sox acquired Badenhop from the Milwaukee Brewers in exchange for minor league pitcher Luis Ortega on Nov. 22.
The 30-year-old went 2-3 with a 3.47 ERA in 62 1/3 innings over 63 relief appearances for the Brewers during the 2013 season. Badenhop closed out the campaign strong, recording a 2.05 ERA over his last 21 games and allowing only five runs during that span.
After being drafted by the Detroit Tigers in 2005, Badenhop was traded to the Miami Marlins, where he spent the first four years of his career. Badenhop was then dealt to the Tampa Bay Rays before the 2012 season before moving on to Milwaukee the following year.
Over the course of his six-year major league career, Badenhop has compiled an 18-20 record to go along with a 3.98 ERA in 280 games.
Terms of the deal were not disclosed.