Parra, 33, posted a 3.90 ERA in 40 appearances with Cincinnati last offseason and did not receive much public interest on the free-agent market. The southpaw joins Aaron Crow as recent bullpen additions to Cubs' camp, and will compete for a spot on the Opening Day roster alongside fellow lefties Clayton Richard, Travis Wood and Rex Brothers.
Parra is a veteran of 8 major-league seasons, and has spent his entire career in the NL Central with the Brewers (2007-12) and Reds (2013-15). He is the owner of a lifetime 29-41 record and 4.90 ERA in that span, but has worked exclusively as a reliever since the 2012 season.
With Parra off the board, teams looking for left-handed relief help will have to turn to options like Matt Thornton, Franklin Morales, Neal Cotts, Joe Beimel and Sean Marshall.