Cardiff announced the signing of Jones on their Twitter page:
Stoke then quickly confirmed the addition of Odemwingie and posted an interview with the striker, who praised the club's fans and "great group of players."
The deal works in favour of both clubs, which are facing a tight relegation battle. Cardiff are bottom of the league while Stoke lay in 14th place with only four points separating them.
Jones joined Stoke in 2010 after Tony Pulis signed him from Sunderland for £8 million. Odemwingie, meanwhile, spent less than 12 months at Cardiff after his £2.25 million arrival under then-manager Malky Mackay.
Both players have had limited opportunities this season, and the move would be a new start for both. Odemwingie, a Nigerian international, has been on Stoke's radar since the summer, before he signed for Cardiff, per BBC Sport.
Speaking to Pete Smith in the Stoke Sentinel, chief executive Tony Scholes said: "We were interested in signing Peter last summer when he left West Brom but we’re really pleased to have finally secured his services."
In a statement on the Stoke website, the club announced Odemwingie had signed an 18-month contract.
Jones has seen his chances limited this season at the Britannia under manager Mark Hughes, and he failed to report for duty when Stoke played Liverpool a fortnight ago, according to The Telegraph's John Percy and Ian Winrow.
The big centre-forward has only played seven times in all competitions for Stoke this season, per ESPN FC, and he has grown increasingly frustrated at his lack of game time.
Jones will add more firepower to Ole Gunnar Solskjaer's new-look Cardiff side, which play Manchester United on Tuesday at Old Trafford.
However, he won't be available for selection until Saturday's home game against Norwich, according to the statement on Cardiff's website.
Cardiff are also expected to announce the signing of Fabio from Manchester United, reports Terry Phillips of WalesOnline.