Sharp was a long term target for Gary Peters, who tried to take over the 30-year-old's contract in December.
A left sided defender was high on Peters' shopping list, after Trevor Challis was released earlier in the summer.
Peters revealed that Scunthorpe had offered terms to Sharp, but he was keen to play first-team football at the Meadow. He also said that number-two Mick Wadsworth was key in the acquisition, having worked with the player at Huddersfield.
Peters told ShrewsWeb: "He's got good experience, is 30-years old and has a great left foot. He can play left-back, central midfield, left midfield and even left-sided centre back."
He continued: "They were trying to get him to stay there but Kevin didn't want to sign and not play so we've made him an offer and he's come here."