London expects to graduate from Michigan State in May.
He ran for 304 yards on 83 carries last season as a backup to LJ Scott, who is returning for his senior season.
London (6-1, 218) started the first six games of his redshirt freshman season in 2015, later missing three games due to injury and finishing third on the team with 500 yards on 119 carries. He rushed 28 times for 120 yards in 2016.
He will join a Tennessee backfield that lost junior running back John Kelly to the NFL Draft after last season. Ty Chandler (305 yards) and Carlin Fils-aime (215 yards) return for the Vols.