In return, Class-A Advanced infielder Javier Betancourt heads to Milwaukee. Also, one or two players to be named later is included in the deal, with one possibly headed to both sides.
Tigers GM Al Avila noted that the team will be sending a player to be named later to Milwaukee but noted that the Tigers might get one as well.
"It could happen that way, but it may not. ... It's complicated," Avila told Jason Beck of MLB.com.
The Tigers have been needing relief pitching for some time now.
Their bullpen posted the third-worst collective Wins Above Replacement in 2015, according to FanGraphs. Thee group's ERA (4th-highest), FIP (T-2nd), and xFIP (1st) were all in the bottom five in baseball.
The team had issues finding a true closer last season. Five players on their team recorded a save.
Joakim Soria, their main closer, is a free agent this offseason and will likely head elsewhere. Even he, however, was not the best at his job, saving 23 games in 26 opportunities, posting a 2.85 ERA and 4.87 FIP.
In Rodriguez, the Tigers will be getting a sure-fire closer.
The 33-year-old has closed almost his entire career, breaking onto the scene as one of the best in 2005, when he saved 45 games. Three years later, he set the single-season record for saves with 62.
Since 2008, Rodriguez has averaged 25 saves a season, but has made a reemergence in the past two years with the Brewers. He was named to the National League All-Star team both seasons.
In 2015, Rodriguez went 1-3 with a 2.21 ERA and 2.91 FIP in 57 innings out of the bullpen, saving 38 games in 40 opportunities. He posted a 62 to 11 strikeout-to-walk ratio.
Rodriguez could be a free agent at the end of the 2016 season, but has a $6 million team option with a $4 million buyout for 2017 that looks almost like a lock to be picked up. Assuming it is, the Tigers will be on the hook for $11.5 million of Rodriguez's salary over the next two years.