He didn't make the Padres' roster in Spring Training and was released.
The Red Sox have Craig Kimbrel as the closer, and Koji Uehara and Junichi Tazawa serving as the primary setup men.
Ever since losing Carson Smith for the season following Tommy John surgery, the Red Sox have been on the lookout for some more bullpen help.
Janssen, 34, will start at a lower-level affiliate and eventually work his way up to Triple-A Pawtucket.
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.