Sharp will take the number three shirt, and is the second defensive signing of the summer following the capture of Ireland U21 international Cliff Byrne on a free transfer from Sunderland.
He came close to joining United last season, but a move failed to materialise when it became clear that no-one was going to come in for out of contract Andy Dawson.
He has signed a one-year deal, and is hoping to mark the season with promotion to the second division.
He told the Scunthorpe Telegraph: "There is no reason this year why we can't go up automatically, I am sure the players are up for it.
"They have been so near, yet so far, in recent times so I think it is about time they got promoted."