Greenberg, 46, replaces Ricky Stokes, who was fired last month after Virginia Tech missed the Big East Conference tournament for the third straight year.
"I believe we have found someone who has extensive head basketball coaching experience and beneficial recruiting ties throughout the Eastern Seaboard," Virginia Tech Athletic Director Jim Weaver said.
According to the Roanoke (Va.) Times, Weaver phoned South Florida Athletic Director Lee Roy Selmon on Wednesday morning and received permission to speak with Greenberg, said USF spokesman Mike Hogan.
The paper also said Weaver had been interested in Rhode Island Coach Jim Baron, but Baron agreed to a new contract with that school and withdrew from consideration on Tuesday.
In seven seasons at South Florida, Greenberg's teams posted a 108-100 record, including a 15-14 mark this year. Greenberg is the only coach in USF history to post a .500 record or better for six straight years. He twice took the Bulls to the National Invitation Tournament, but failed to make the NCAA Tournament.
Greenberg coached at Long Beach State for six seasons before going to South Florida. He earned one NIT and two NCAA Tournament berths at Long Beach.
"I am very excited about the challenge and opportunity presented at Virginia Tech," Greenberg said. "Everything is in place to have one of the elite programs in the Big East."
Greenberg, a 1978 graduate of Fairleigh Dickinson, also has been an assistant at Columbia, Pittsburgh, Miami, and Long Beach State. Pittsburgh made the NCAA tournament in two of Greenberg's three seasons there.
Virginia Tech won 16 games in its first season under Stokes but slumped to 8-19 in 2000-01 and was a mere 45-70 in his four-year tenure.