Alford, who was the Fighting Irish's running backs coach and recruiting coordinator, told Scout.com that he will be the Buckeyes' assistant head coach and running backs coach.
The move is Notre Dame's latest staff departure this week, as secondary coach Kerry Cooks left for Oklahoma and quarterbacks coach Matt LaFleur is expected to leave for the NFL's Atlanta Falcons.
Alford is also the third different Notre Dame assistant to leave for Ohio State since head coach Urban Meyer arrived there before the 2012 season, joining Ed Warinner and Tim Hinton.
Drayton had left Ohio State after national signing day to join the Chicago Bears' staff.
Alford had been the lone holdover from Charlie Weis' staff at Notre Dame, lasting six total seasons with the Irish. As Notre Dame's recruiting coordinator the last three seasons, Alford was instrumental in the Florida area, having just landed ESPN No. 5 running back Dexter Williams this cycle.