Blades beat off competition for Sharp from Norwich, Sheffield Wednesday, Wolves and Preston.
Sharp had left Bramall Lane in 2005 after just two substitute appearances to join Scunthorpe.
But under the terms of that deal, the Blades will receive 25% of any transfer fee involving the striker.
Blades's chairman Terry Robinson said: "We made it known to Billy's representatives eight weeks ago that we would be interested in bringing him back here.
"Billy's glad to be back, he knows what we're about and we hope he'll score plenty of goals for us."