Varnado won the award Friday during Final Four festivities in Indianapolis.
The 6-foot-9 Brownsville, Tenn., native finished his career as the NCAA's blocks leader with 564 and is the only player to have 1,000 points, 1,000 rebounds and 500 blocks.
Varnado called the award "humbling."
This season he led the Bulldogs to 24 wins and the Southeastern Conference Western Division title, and finished with 170 blocks to tie his own SEC record.
The award is named for Driesell, a Hall of Fame coach whose 786 wins rank ninth among Division I coaches.