Newspapers in Kentucky and Minnesota said they had confirmed the move. The St. Paul Pioneer Press said the Gophers would introduce Smith at a news conference Friday.
Minnesota has not had a head coach since Dan Monson, seven games into his eighth season at Minnesota, resigned Nov. 30. Jim Molinari handled the team on an interim basis this season. The Gophers ended up 9-22 overall and 3-13 in the Big Ten.
Smith coached Kentucky, one of the most storied programs in college basketball, for 10 seasons, building a 263-83 record and qualifying for the NCAA tournament each season. The Wildcats won the NCAA championship under Smith in 1998.
In 16 seasons as a head coach at Tulsa, Georgia and Kentucky Smith has a 386-144 record.