Edmonds comes to the Reds batting .286 with eight home runs and 20 RBI in 73 games this season.
The 40-year-old is marking a return to the game after sitting out the entire 2009 season, originally signing a minor league deal with Milwaukee in January and then making the Brewers' roster out of spring training.
Edmonds is a .285 career hitter with 390 homers and 1,196 RBI collected over an 18-season career with the Los Angeles Angels, St. Louis, San Diego, Chicago Cubs and Brewers.
Dickerson was placed on the disabled list after hitting .205 in 44 at-bats this season with the Reds.
He broke a bone in his right hand in April and last month began a rehabilitation assignment at Class AAA Louisville, where he hit .442 with three homers and seven RBI in 13 games.