The 30-year-old defender has not appeared for parent club Wolves this season after being placed on the transfer-list in the summer following the Midlanders' relegation to Sky Bet League One.
But Johnson, who played under Owls boss Jones for three seasons at Cardiff before being sold to Birmingham for £5million in 2009, could make his first appearance for Wednesday on Saturday against the Blues at St Andrew's.
"I'm a footballer and I just want to play football," Johnson told Wednesday's official club website.
"The gaffer has given me the chance to come here and I'm going to take it with both hands and I'm looking forward to it.
"I had great times with the manager at Cardiff and he has put his faith in me again and I won't be letting him down."
Johnson, who started his career at Wycombe before spells at Cardiff, Birmingham and Wolves, is hoping to make a real impact during his three-month stay at Hillsborough.
He added: "I know what the Championship is all about and I have massive belief that I can do the business at Sheffield Wednesday.
"This is a really good move for me and when the opportunity came around, I knew it was right for me.
"I'm looking to come here and play games. There are 17 games that I'm here for throughout the loan period and I'm just looking to doing as well as I can for the club and get myself back playing."