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.
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.