The Clippers received forward Carlos Delfino, center Miroslav Raduljica and a 2015 second-round pick.
Dudley averaged 6.9 points and 2.2 rebounds over 74 games (43 starts) last season.
The seven-year veteran, who was selected 22nd overall by Charlotte in 2007, owns career averages of 8.7 points and 3.4 rebounds, while shooting 46.9 percent from the field in 523 career games with Charlotte, Phoenix and the Clippers.
Delfino missed all of last season with a foot injury that he suffered during the 2013 NBA playoffs with the Rockets. The 31-year-old native of Argentina has averaged 8.1 points and 3.6 rebounds over eight seasons with Detroit, Toronto, Milwaukee and Houston.
Raduljica scored 3.8 points per game with 2.3 rebounds over 48 games for the Bucks last season.