The 32-year-old right-hander had been released by the San Francisco Giants Sunday.
Brower was 2-1 with a 6.53 ERA in 32 games with the Giants this season and had been tagged six runs on 10 hits in 6 1/3 innings in his last three appearances.
"We've always liked him in the bullpen out there," Manager Bobby Cox said on the team's Web site.
"We don't see that team (San Francisco) that often, and sometimes you miss some of their pitchers when you play them only three games. He's a kid that would help set up for (the Giants), pitched in the middle, and even closed occasionally," Cox said.