Oats, 44, replaces Avery Johnson, who parted ways with the Crimson Tide earlier this week after four seasons in Tuscaloosa.
"We are thrilled to welcome Nate and Crystal Oats and their three daughters to The University of Alabama," athletic director Greg Byrne said. "I have been watching Coach Oats for the last few years as he has led the University at Buffalo to unprecedented heights. His commitment to developing the student-athlete both on and off the court was what really stuck out. As we spoke to some of the best college and pro basketball minds in the country, his name came up time and time again. Coach Oats will hit the ground running starting tonight, and we look forward to him having a long and successful career with the Alabama Crimson Tide."
Oats has led Buffalo to the second round of the past two NCAA tournaments, beating Arizona in the first round last season and blowing out Arizona State this season. The Bulls' season ended against Texas Tech in the second round last weekend.
Buffalo went to three NCAA tournaments in Oats' four seasons at the helm, going 96-43 overall. Buffalo lost just five Mid-American Conference games combined over the past two seasons.
Oats signed a contract extension with Buffalo two weeks ago that would have kept him with the Bulls through 2024. The extension raised his buyout amount to $750,000.
Before becoming the head coach at Buffalo, Oats was an assistant under Bobby Hurley for two seasons with the Bulls. He also spent 11 seasons as the head coach of Romulus High School (Michigan).
Top assistant Jim Whitesell will serve as interim head coach as Buffalo conducts a head-coaching search.