Rodriguez, who was acquired on July 12 of last season in a trade from the New York Mets, had a mutual option worth $17.5 million dollars for next season but will instead receive a $4 million buyout.
The major-league record holder for saves in a single season (62) had a 6-2 record with a 2.64 ERA and 23 saves last season, serving mainly as an eighth- inning man with Milwaukee.
Betancourt's $6 million club option was denied by Milwaukee and he will receive a $2 million buyout from the Brewers.
He was the third-ranked shortstop in the majors with 21 errors last season, but also ranked second among shortstops with 68 runs batted in through 152 games.
The two players will join fellow Brewers first baseman Prince Fielder, infielders Craig Counsell and Jerry Hairston Jr., outfielder Mark Kotsay and relievers LaTroy Hawkins and Takashi Saito as free agents.