The 31-year-old Gyorko has played seven major league seasons with San Diego, St. Louis and the Los Angeles Dodgers.
He was hampered by injuries in 2019 and batted .174 with two homers in 62 games with the Cardinals and Dodgers. He had been a steady contributor prior to last season and hit 30 homers for St. Louis in 2016.
"We think he fits our team really well with a right-handed bat and the ability to play multiple positions," general manager David Stearns said, adding "we believe he's healthy now."
A right-handed hitter with a sharp defensive reputation, Gyorko is expected to split time with left-handed hitting Eric Sogard at third base after Mike Moustakas and Travis Shaw left Milwaukee as free agents. Gyorko has also played second base, first base and shortstop, although he's unlikely to play much short going forward.
Milwaukee designated right-hander Jake Faria for assignment. Stearns said he hopes Faria clears waivers and remains in the organization.
The club settled with catcher Omar Narvaez on a one-year deal for $2,725,000.
The Brewers exchanged salary arbitration figures with All-Star closer Josh Hader -- he asked for $6.4 million and was offered $4.1 million -- and left-hander Brent Suter, who sought $1.25 million and was offered $825,000.