Badenhop, 30, made 63 appearances for the Brewers in 2013 and posted a 3.47 ERA with a 1.19 WHIP. In 62 1/3 innings, he walked just 12 hitters.
Badenhop will be entering his seventh season in the Majors with his fourth team. Aside from Milwaukee, he has played for Florida and Tampa Bay.
With Badenhop's deal completed, the Red Sox now have four remaining arbitration-eligible players: first baseman/outfielder Mike Carp, infielder Jonathan Herrera, left-hander Andrew Miller and right-hander Junichi Tazawa.
Players who filed for arbitration and their clubs will exchange proposals for a one-year contract on Friday. Each player to file is considered signed for the 2014 season, but there's no set salary until a deal is reached. If no settlement ensues, the case goes before an arbitration panel, which awards the player with either his salary proposal or the club's after each side states its case. Arbitration hearings will be held from Feb. 1-21.
All 133 players who filed for arbitration last year settled with their respective clubs and avoided hearings.
AJ Cassavell is a reporter for MLB.com. Follow him on Twitter @ajcassavell. This story was not subject to the approval of Major League Baseball or its clubs.