Crawford, a 6-foot-5 shooting guard, announced he was leaving Memphis earlier this month, shortly after star forwards Dedric Lawson and K.J. Lawson left the program. Only two key players from this past season are set to return to the Tigers next season.
Crawford averaged 12.8 points and 4.4 rebounds in 2016-17.
Ole Miss coach Andy Kennedy said in a statement that Crawford is "a versatile guard capable of playing either backcourt position. He is big, strong and athletic with the ability to make plays both on the offensive and defensive ends.''
The Associated Press contributed to this report.