The Brewers acquired Rodriguez from the New York Mets in a July trade. He will get a $4 million buyout rather than receiving $17.5 million through a mutual option.
The reliever, who holds the major-league record for saves in a single season (62), compiled a 6-2 record with a 2.64 ERA and 23 saves last season.
Betancourt, meanwhile, will get a $2 million buyout after Milwaukee turned down a $6 million club option for 2012.
The shortstop made 21 errors last season but also ranked second at his position with 68 runs batted in through 152 games.