The Yorkshire side have paid £1.15millon for Sharp, who spent last season on loan at the club from the Blades.
He had failed to break into the first-team at his hometown club, after returning to them from Scunthorpe in 2007.
"Everyone knows what a difference Billy's goals made to us last season," said Sean O'Driscoll, the Rovers manager.
"On top of that he very quickly became an integral and popular member of the squad, always displaying a great attitude and willing to put in a real shift for the good of the team.
"He is one of those characters who is great to have around a football club and he just loves playing football and scoring goals."