The Blue Devils formally announced Obi's transfer Friday.
Obi is a 6-foot-9, 265-point post player who must sit out next season. He will have three years of eligibility beginning in 2015-16.
He averaged 11.4 points and a Conference USA-leading 9.3 rebounds as a freshman at Rice, and reached double figures in 17 of 30 games.
He becomes Duke's fifth Division I transfer under head coach Mike Krzyzewski, joining Dahntay Jones, Roshown McLeod, Seth Curry and most recently Rodney Hood.