Rodriguez tallied 38 saves in 40 chances and had a 2.21 ERA and 62 strikeouts in 57 innings last season for the Brewers. Overall, K-Rod has 386 career saves over 13 major league seasons with four teams.
"It's something that me and my family are looking forward ... knowing a little bit more about my future, where I'm going to be at next year," Rodriguez said.
Detroit general manager Al Avila said the Tigers might also receive a player to be named in the deal, but that's not certain.
"We had explored a lot of the different options that are presented out there," Avila said. "There's a lot of free-agent pitchers, none of which really have extensive closing experience. We also checked with a lot of major league clubs that are entertaining the idea of a possible trade."
Rodriguez, who turns 34 in January, is due $5.5 million in 2016 with a $6 million option for 2017 that includes a $4 million buyout. He has been durable for far longer than most relievers and remains effective because he remade himself as a changeup guy even as his fastball has dipped to average.
According to Fangraphs.com, Rodriguez threw fastballs on only about 45 percent of his pitches this year, while throwing a changeup about 43 percent of the time.
"When I look at Frankie, I see kind of a little bit of a Trevor Hoffman," Tigers manager Brad Ausmus said. "Both of these guys, they came up throwing 95-plus miles an hour and could basically throw the ball by guys. ... Frankie, like Trevor, has just turned to the changeup -- both of them had tremendous changeups, swing-and-miss changeups -- and he's reinvented himself and become equally as successful."
The Brewers will receive minor league infielder Javier Betancourt and a player to be named.
Despite having won two AL Central titles over the past three seasons, the Tigers' bullpen has ranked 27th in the majors with a 4.17 ERA during that span. Detroit finished last in the AL Central in 2015 after four consecutive division titles.
The Tigers this month declined their $10 million option on Joe Nathan. He spent two years with Detroit, struggling in 2014 and missing almost all of 2015 with an elbow injury.
Betancourt, 20, hit .263 with 17 doubles and 48 RBIs with Class A Lakeland in 2015.
Milwaukee went 68-94 this season and felt it could trade Rodriguez to build for the future.
"We've stated our intentions many times in the past," new Brewers GM David Stearns said. "We're looking to acquire as much young, quality, controllable talent as we can, and we think we took a nice step forward with the deal."
ESPN MLB Insider Keith Law and The Associated Press contributed to this report.
Tigers land veteran closer Francisco Rodriguez
David Schoenfield discusses how Francisco Rodriguez has rejuvenated his career, and his likely role with Detroit's bullpen in 2016.