Greenberg spent nine seasons as the Virginia Tech head coach with one NCAA tournament appearance.
It's reported that Johnson has accepted the position less than two weeks after leaving Virginia Tech for an assistant job at Clemson. Johnson informed Clemson that he would be accepting the Virginia Tech job after interviewing over the weekend.
Before Greenberg was fired on April 24, Virginia Tech athletic director Jim Weaver said he had tried to persuade Johnson to stay by matching his salary offer from Clemson. But Johnson declined, telling Weaver it wasn't about the money.
Johnson, a Virginia native, worked as an assistant at George Mason, Penn State, College of Charleston, Elon and Old Dominion before coming to Virginia Tech in 2007.
Johnson will try to keep the Hokies' top recruits, Marshall Wood from Lynchburg, Va., and Montrezl Harrell from Tarboro, N.C. They would join returning guard Erick Green, forward Cadarian Raines and Dorian Finney-Smith.
The Hokies will look to improve their 16-17 overall record, 4-12 in the ACC.