The 6-foot-7, 200-pound shooting guard, who averaged 9.3 points and 5.0 rebounds this season, had told Kansas coach Bill Self before making his decision public Wednesday.
"It's always been a dream to play in the NBA. This is an opportunity to play against the best in the world and expand my game in hopes of someday becoming one of those great players," Oubre said in a statement. "It's been a great year. I've been blessed to be here at the University of Kansas.
"I was blessed to go through the things that I went through and I was blessed to play for coach (Bill Self). He taught me a lot this year, the little things that will help out my game a lot."
Oubre, who scored nine points as the Jayhawks lost to Wichita State in the NCAA tournament's round of 32, was an All-Big 12 honorable mention selection.
"This should come as really no surprise to anybody that has followed us," Self said in a statement. "Kelly came in being well thought of by NBA personnel and certainly, nothing has changed in that regard. In the time he was here he's been a great ambassador, a great teammate and, obviously, a very talented player."