Montgomery has been calling the plays for one of the most prolific offenses in college football. Baylor is the only team in FBS to be ranked in the top four in the country in total offense each of the last four seasons.
The Bears averaged 48.8 points and 581.3 yards per game this season under Montgomery, who just completed his seventh season and also served as the quarterbacks coach.
"I've always wanted to be a head coach, but my family and I knew that it would take the right opportunity to get me to leave Waco. Tulsa is that special opportunity," Montgomery said in a statement. "There is a lot of work to get done and trust me, I'm already on it. Get ready for some fun, fast and physical football."
The 42-year-old Texan has spent most of his career as an assistant to Baylor coach Art Briles, first at Stephenville (Texas) High School and then at Houston (2003-07) and Baylor.
"We are extremely pleased to have Philip Montgomery as our head football coach," said Tulsa athletic director Derrick Gragg said in a statement. "Coach Montgomery has an outstanding background as a collegiate coach and recruiter. He is one of the bright offensive minds in college football and has coordinated explosive offenses at both Houston and Baylor."
Montgomery was a finalist for the Broyles Award, given to the nation's top assistant coach, in 2013.
He replaces Bill Blankenship, who was fired Dec. 1 after a 2-10 season in 2014 and a 24-27 record at Tulsa over four seasons.
Tulsa went to eight bowls between 2004-12, played in the Conference USA championship game four times and won a championship twice. Since their last title in 2012, the Golden Hurricane have won five games.
The Associated Press contributed to this report.