In the deal, Milwaukee will send Toronto a lottery-protected first-round pick in the 2017 draft, via the Los Angeles Clippers, as well as the No. 46 pick in Thursday's draft.
The details of the trade were first reported by Marc Spears of Yahoo! Sports.
Over 82 games with Toronto last season, Vasquez averaged 9.5 points and 3.7 assists while shooting 40.8 percent from the field.
The Raptors went 49-33 and earned the No. 4 seed in the Eastern Conference, while the the Bucks finished 41-41 and earned the No. 6 seed.