Jones, 31, was believed to be the Iron's top earner and the club have forsaken a transfer fee to get him off the wage bill.
He ended last season on loan at the Owls, making eight appearances, and has signed a two-year contract at Hillsborough.
Despite joining the club for a substantial outlay from the Scottish Premier League side Hibernian in July 2009, he has often been a peripheral figure at Glanford Park due to a succession of injuries which limited him to 48 appearances in all competitions across two seasons.