Odemwingie has put pen to paper on an 18-month contract with the Staffordshire outfit and Potters manager Mark Hughes is hopeful of including him in his squad for Wednesday's Barclays Premier League encounter with Sunderland at the Stadium of Light.
Hughes told www.stokecityfc.com: "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."
Cardiff also confirmed the exhange deal on their Twitter feed.
The Welsh side said Jones' move had been finalised, subject to Football Association clearance, and that he will be available for selection for the first time on Saturday when the Bluebirds host Norwich.
News about the two players swapping clubs emerged on Saturday when Stoke announced they had reached an agreement with Cardiff over the deal for the pair.
Jones had not been involved in either of the Potters' two games prior to that, with him having sent a text message to Hughes the night before the clash with Liverpool on January 12 to say he was unavailable for the fixture.
That resulted in the 29-year-old Trinidad and Tobago international being fined two weeks' wages and meant he was not considered for selection for the next match, against Crystal Palace.
Jones joined Stoke on a permanent deal in 2010, having previously spent a brief loan spell with them.
He has scored five times in 10 appearances for them this season, with all the goals coming in cup competitions.
Nigeria international Odemwingie only signed for Cardiff in September.
The 32-year-old has scored twice in 17 appearances for them since, with his last goal coming in October. He was previously with West Brom.
Odemwingie told Stoke Player: "Maybe in the past few months I didn't get too many goal-scoring opportunities, but I am sure that will change here at Stoke.
"One of my strongest qualities is being able to put the ball into the back of the net, with either my right foot or my left foot, and I intend on doing that regularly here.
"I like to get myself into good positions on the field whereby I can get opportunities and I know that with the quality of players here at the club there will be days where we do create a lot of chances to score the goals.
"I feel I am a different player to Kenwyne Jones. He is more of a target man, but I am somebody who likes the ball at my feet and I also like to get in behind the defence as often as possible too.
"I am sure that the manager and his staff know about me and I am certain they will use me to my strengths.
"They are very knowledgeable people and they must feel that I can bring something different to the team. That gives me a lot of confidence and belief in myself."
It seems Stoke could soon have another new face among their ranks, with cameras having caught footage of Blackpool winger Tom Ince - accompanied by his father Paul - at the Potters' training ground on Tuesday.
It was reported that the England Under-21 international held talks with Hughes over a possible deal.
Ince was in discussions with Swansea on Monday and has been linked with various Premier League clubs.
Meanwhile, Stoke's United States midfielder Maurice Edu has returned to his home country by joining Philadelphia Union on a one-year loan deal, which includes an option for the Major League Soccer side to purchase the 27-year-old.
Edu has made just one appearance for the Potters, as a substitute last season, since joining them in the summer of 2012 and spent part of that campaign on loan at Bursaspor in Turkey.