Jones, the Iron's record signing, will stay at Hillsborough until the end of the season.
He will go straight into the Owls squad that travels to take on Southampton on Saturday evening.
The match, which is being shown live on Sky Sports 2, will see him up against familiar faces in the former Iron manager Nigel Adkins, assistant Andy Crosby and forward Jonathan Forte.
Adkins brought Jones to Glanford Park from the Scottish Premier League side Hibernian at the start of the 2009-10 season.
Jones has made 48 appearances in his two seasons in North Lincolnshire, scoring twice.
There is no indication from either club whether the move could be made permanent in the summer.