Under the terms of the deal, Redick, an unrestricted free agent, moved from the Bucks to the Clippers, who will sign him to a reported a four-year, $27 million contract.
The Clippers, meanwhile sent point guard Bledsoe and veteran forward Butler to the Phoenix Suns in exchange for swingman Jared Dudley.
To complete the trade, Milwaukee received pair of future second-round draft choices from each of the other two teams.
Redick had a breakout season in 2012-13, averaging 14.1 points and 3.8 assists per game while splitting time between the Bucks and Orlando Magic. He boasts a 3-point career accuracy of 39 percent.
Bledsoe, who last season backed up superstar guard Chris Paul for the Clippers, averaged 8.5 points, 3.0 rebounds and 3.1 assists in nearly 20 1/2 minutes per game.
Dudley averaged 10.9 points, 3.1 rebounds and 2.6 assists as for Phoenix last season, while two-time all-star Butler posted 10.4 points per game in 2012-13 for Los Angeles.