Reynolds, 30, batted a combined .220 last season for the Indians and the Yankees but banged 21 home runs and knocked in 67 runs in 135 games. His last 36 games were with the Yankees.
Reportedly the Yankees, Nationals, Twins, Rangers and Orioles also had some interest in the right-handed slugger. He's hit 202 homers in his 988 big league games, including 44 for the Diamondbacks in 2009, when he also had 102 RBIs.
His power production usually has been accompanied by low averages -- his career mark is .233.
The Brewers are anxious to find a productive bat at first base and Reynolds, although most of his career has been spent at third base, has plenty of experience there, too. After Prince Fielder went to the Tigers, Corey Hart was the primary first baseman in 2012, but he missed all of last season after surgery on both knees before being acquired by the Mariners.
In 2013, the Brewers used seven different first basemen, mostly Yuniesky Betancourt and Juan Francisco, but combined they had the lowest OPS in the Majors at that position.
"We want to try to get away from that and take it into a much smaller group, try and get some consistency there," said Gord Ash, the Brewers' assistant general manager.
Reynolds was drafted in the 16th round of the 2004 First-Year Player Draft out of the University of Virginia by the Diamondbacks. He made his debut with the D-backs in 2007 and was an immediate success, joining the club in mid-May and hitting .426 with four homers and 15 RBIs for the rest of the month.
His big 2009 season -- he not only led the D-backs with 44 homers but also with 24 stolen bases -- got him named to the Sporting News' National League All-Star team. But after falling off the next year, he was traded to the Orioles.
Along with power, he's posted some high strikeout marks. In fact, in 2010, he became the first non-pitcher to have more strikeouts (211) than his batting average (.198). In 3,418 Major League at-bats, he has 1,276 strikeouts.
"He's got terrific power, of course, and with that power comes some strikeouts, which we're well aware of, but he's a pretty good defender," Ash said. "He's shown capability at both first and third base, and he's a good veteran bat to add to our lineup. But he's got to make the team -- he signed a Minor League contract."
Reynolds will be competing with Francisco, a left-handed hitter, for the job. Francisco played 67 games at first base last year and hit .221 with 13 homers and 32 RBIs in a total of 89 games with the Brewers.
Also in the picture is Sean Halton, who played 25 games at first for the Brewers with a .238 average, four homers and 17 RBIs. Halton, a right-handed batter, spent most of last season with Triple-A Nashville and had a .273/11/51 line. Taylor Green, who missed all of last season after undergoing hip surgery for a Spring Training injury, is returning and could figure at first base. He's a left-handed hitter who had a .184 average in 58 games for the 2012 Brewers.