Badenhop posted a 3-2 record and 3.03 ERA in 66 appearances out of Tampa Bay's 'pen last season. He spent his first four big league campaigns with the Marlins before they traded him to the Rays last December. In all, Badenhop has compiled a 16-17 mark and 4.08 ERA in 217 career outings (10 starts).
Milwaukee's bullpen ranked last in baseball in 2012 with a 4.66 ERA. Brewers relievers also racked up a league-high 29 blown saves.
The Rays had tendered Badenhop a contract for the 2013 season prior to Friday's 11:59 p.m. ET deadline. The reliever earned $1.075 million last year.
The Brewers signed Mondesi as a non-drafted free agent in June 2010. He played parts of three seasons in the organization -- the first two with its Dominican Summer League squad and this past season with its Rookie League affiliate in Helena, Mont. In 2012, he batted .231 with five homers and 32 RBIs in 68 contests.
Mondesi's father, Raul Sr., played with seven big league clubs from 1993-2005 and tallied 271 career homers.