The 35-year-old right-hander, cut loose by Boston earlier this month after going 0-1 with a 6.39 ERA in nine relief appearances, worked out for the Brewers' staff in Washington on Sunday. He traveled back to Milwaukee with the team to take a physical.
The Brewers are looking to bolster a pitching staff that has been struggling with injuries and inconsistency all season.
To make room for Tavarez on the 25-man roster, Milwaukee optioned left-hander Zach Jackson to Triple-A Nashville.
The Brewers will be Tavarez's ninth team. He has pitched for Cleveland, San Francisco, Colorado, the Chicago Cubs, Florida, Pittsburgh, St. Louis and Boston in his 16-year career.