For general manager Jon Horst, Budenholzer had always been his top target, and a finalized contract is expected to be completed soon, league sources said.
The person confirmed the agreement with the former Atlanta Hawks coach on Wednesday.
Toronto fired Dwane Casey, who may win Coach of the Year, after Cleveland swept the Raptors in the second round.
United States identifies suspect in major leak of Central Intelligence Agency hacking tools
Despite searching the suspect's NY apartment, prosecutors say they now lack the evidence to charge Schulte. The government immediately had enough evidence to establish that he was a target of that investigation.
With Budenholzer having joined the Bucks, the Raptors' search for a new coach continues onward. He pulled out of contention for the Suns job after several conversations with ownership and management. Budenholzer had been the Hawks' president of basketball operations - until surrendering front-office control with the arrival of general manager Travis Schlenk in the spring of 2017.
Budenholzer was named the NBA Coach of the Year in 2014-15, but agreed to part ways with the Hawks after the season.
Budenholzer went 213-197 in his five seasons in Atlanta, leading the team to four playoff appearances before this season's 24-58 record.
The Bucks lost to the Celtics in seven games in the first round of the playoffs.