Weber State coach Randy Rahe announced the move Wednesday.
The 6-foot-9, 205-pound Chapman played in 36 games last season at Utah and averaged 4.4 points and 2.8 rebounds. He has two years of eligibility remaining, but must sit out the 2016-17 season due to NCAA transfer rules.
Chapman was surpassed by fellow sophomore Kyle Kuzma on the depth chart last season and the Utes could have even more competition at the position next season.
Weber State finished with a 26-9 record last season and advanced to the NCAA tournament after winning the Big Sky regular-season and tournament championships.