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Sharp was released by United boss Brian Laws in May after making around 60 appearances for the club, scoring twice.
Sharp joined Scunthorpe in June 2003 following his release from Huddersfield Town and the player made a promising start as he replaced Hull City's Andy Dawson as the Iron's left back.
A pre-season injury in 2004/05 saw Sharp struggle to regain his place in the team, as former deputy Lee Ridley made the spot his own.
Sharp only made four starts last season, and the ex-Leeds and Wigan man was linked with moves to Mansfield and Shrewsbury during the campaign but nothing materialised until now.
Shrews boss Peters said of his new signing: "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 and will be another good addition to the squad.
"He's a good defender but he's also a good pro and we've just taken on three 30-year old pros who are tremendous example to the lads.
"They live the right way, do things the right way, do things at the right time and they'll make our young kids better.
"He's got definite quality and straight away with his left-foot we've got a free-kick taker and a corner taker."