Nigeria international Odemwingie, who only moved to the Bluebirds from West Brom last September, has signed an 18-month deal at the Britannia Stadium and is expected to be available for the Potters' Premier League game at Sunderland on Wednesday.
His arrival sees Jones, an £8 million arrival from Sunderland in August 2010, move in the opposite direction.
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"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 goalscoring 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 that 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," he remarked.