The Bucks are expected to send 43rd overall pick Ricky Ledo and a 2014 second-round pick to Philadelphia for Wolters. The trade is expected to be completed sometime Friday.
The trade was confirmed late Thursday by Allegiant Athletic Agency, which represents Wolters.
"Being drafted to play in the NBA is a dream that I've worked my entire life to achive," Wolters said in a statement released by the agency. "Milwaukee is a great organization and I'm very appreciative of this opportunity.
"I can't wait to start my career as a Buck."
Originally picked by Washington with the 38th overall pick, Wolters was traded to Philadelphia along with the 54th overall pick in exchange for Glen Rice Jr. According to reports, Ledo could be headed to Dallas from Philadelphia.
Wolters, 22, averaged 22.3 points, 5.6 rebounds and 5.8 assists per game last season for South Dakota State, shooting 48.5 percent from the field and 37.9 percent from beyond the arc.
Ranked as the 26th overall prospect in the draft by Draft Express, Wolters would help Milwaukee's backcourt, as the Bucks currently have just one guard under contract for next season.