But boss Laws told the Iron's official website: "I just want to clarify that we did not offer Kevin a contract but I would also like to wish him well with his new club."
Sharp said of his time at Glanford Park last season: "It was a mixed season for me last season, I started badly in pre-season as I had to have an operation on my ankle to clear out some wear and tear.
"During my time out the team were doing well and were unbeaten so there's no way the manager could make any changes.
"I only made a handful of games last season and that was disappointing as we got promoted and I wasn't a part of that.
"Scunthorpe wanted me to stay but I think it's time to move on and try something else and Shrewsbury have given me a good chance to do that."