Nigeria international Odemwingie, who only moved to Cardiff from West Brom last September, has signed an 18-month deal at the Britannia Stadium and is expected to be available for Stoke's Premier League game at Sunderland on Wednesday.
Odemwingie's arrival sees Jones, an £8 million arrival from Sunderland in August 2010, move in the opposite direction.
Stoke manager Mark Hughes expressed his excitement at the capture of Odemwingie, who scored a solitary Premier League goal for Cardiff in 15 appearances.
Hughes told the club's official website: "We're delighted to have signed Peter. Things haven't perhaps gone as well for him at Cardiff as he would have hoped and he's really keen to start afresh with us.
"He has a good goal-scoring record in the Premier League and will bring a different dimension to our attacking options.
"I've no doubts he will prove to be an excellent addition to our squad."
Tony Scholes, Stoke's chief executive, confirmed the club had been keen to land Odemwingie in the previous transfer window.
"We were interested in signing Peter last summer when he left West Brom but we're really pleased to have finally secured his services," said Scholes.
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