The seven-year veteran was dealt by the Los Angeles Clippers on Tuesday in exchange for forward Carlos Delfino, backup center Miroslav Raduljica and a 2015 second-round draft pick. The Bucks are also receiving a conditional 2017 first-round pick.
Dudley averaged 6.9 points last year in his only season with the Clippers. The former Boston College star is averaging 8.7 points a game in his career.
Delfino signed as a free agent last year with Milwaukee but never played a game because of a foot injury.
The 7-foot-1 Raduljica averaged 3.8 points in 2013-14.
Milwaukee also announced Tuesday that it had signed second-round draft pick Damien Inglis. The 31st overall selection played last season in France.