Sharp, 24, returned to Bramall Lane from the Iron in 2007 after two impressive seasons at Glanford Park, but has struggled to make an impact at his boyhood club.
He spent last season on loan at Doncaster Rovers , where he scored 15 goals in 35 appearances.
Doncaster made an attempt to make the move permanent this summer but only Burnley had an offer accepted.
Sharp held talks with the Clarets, where he would be reunited for Brian Laws whom he worked under at Glanford Park, but turned down the move. Kevin Blackwell, the Sheffield United manager, welcomed the decision.
"Burnley made an acceptable offer but the move didn't seem quite right to Billy. He's a great lad and playing for the Blades means so much to him but that desire to succeed for his hometown club can be a bit of a burden for him to carry at times because everyone knows he wants to do well here," he said.
"No manager likes to lose good players and if he does decide to stay he can only make our squad stronger in a tough and unrelenting division in which quality and strength in depth count for so much."