The Athletics gave up outfield prospect Andre Ethier.
Bradley, 27, suffered through an injury-plagued 2005, hitting .290 with 13 homers and 38 runs batted in.
In 2004, the Dodgers took a chance on Bradley, who had shown the potential to be an outstanding player. His two years in L.A. were mired by clubhouse problems and arguments between Bradley and management.
Bradley in 2003 with Cleveland hit 10 home runs and batted .321 with 56 RBI and 17 stolen bases. Bradley, who is recovering from knee surgery, is a .269 career hitter with 54 home runs, 233 runs batted in and 54 stolen bases while also playing with Montreal.
Perez, a 25-year-old native of the Dominican Republic, hit a team-leading .297 in 98 games for the Dodgers last season.