"I am honored and humbled to be recognized by the Coaches, they are a great group of people that I admire and respect," Donovan said in a statement.
In his statement, Budenholzer congratulated Donovan and thanked his coaching peers for their votes and support.
Toronto Raptors coach Nick Nurse finished third in the race -- and just one vote away from creating a three-way tie, sources said.
"Those guys obviously did a great job," Nurse said of Budenholzer and Donovan on Monday during a video conference call. "You can't argue with the Bucks' record and how great OKC did after everybody expected lower expectations for them, so those guys are very deserving."
The award, named in honor of longtime NBCA executive director Michael Goldberg, is voted on by the NBA's 30 head coaches, with each coach voting for a single winner. This year's voting was based on games played through March 11, when the season was paused because of the coronavirus pandemic.
Budenholzer, the NBCA's 2019 winner, has led the Bucks to the league's best overall record at 54-13 and the No. 1 seed in the Eastern Conference.
Donovan has the Thunder sixth in the Western Conference at 41-24 in a season when some wondered whether they could reach the playoffs.
"Mike led the Bucks to the best record in the league for a second straight season and Billy became just the fourth active Head Coach to lead his team to the playoffs in each of his first five seasons," Dallas Mavericks coach and NBCA president Rick Carlisle said in a statement. "To win the vote of our peers makes the Michael H. Goldberg NBCA Coach of the Year Award one of the most meaningful in all of pro sports."
This is the second time the NBCA has had a tie, along with 2017 with Houston's Mike D'Antoni and Miami's Spoelstra.
The NBA also gives a coach of the year award -- the Red Auerbach Trophy -- based on a vote of the league's media. That will be released at a later date.
ESPN's Nick Friedell contributed to this report.