The Potters announced on Tuesday they had completed the signing of the 32-year-old from Cardiff as part of a player-exchange deal that sees fellow striker Kenwyne Jones moving in the opposite direction.
And Odemwingie, who is on an 18-month contract with Stoke, could make his debut in Wednesday's league match at Sunderland.
The Nigeria international only joined Cardiff in September and after scoring twice in his first four games as a Bluebirds player, he did not manage another goal in the 13 further appearances he made for the Welsh outfit.
Prior to that he was with West Brom, for whom he scored a total of 30 top-flight goals over three seasons, with 15 of them coming in 2010/11, his first campaign in English football.
And regarding what he might deliver for his new club, 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 am sure that the manager (Mark Hughes) 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."
He added: "I am really hoping for a long and successful time with Stoke City."
Hughes has already brought in Manchester City frontman John Guidetti on loan during the current transfer window.
Another striker has also joined in Juan Agudelo, although he is spending time on loan with FC Utrecht while the Potters try to secure a work permit for him, and midfielder Stephen Ireland has signed a permanent deal as well having previously been on loan from Aston Villa.
On his latest recruit, Hughes said: "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."
It seems Stoke could soon have another new face among their ranks, with cameras having caught footage of Blackpool's Tom Ince at the Potters' training ground on Tuesday.
It is reported that Ince held talks with Hughes over a possible deal. The winger was in discussions with Swansea on Monday and has been linked with various Premier League clubs.
Meanwhile, Stoke midfielder Maurice Edu has joined Philadelphia Union on a one-year loan deal, which includes an option for the Major League Soccer side to purchase him.
Captain Ryan Shawcross is expected to play on Wednesday with protection on a wrist he has fractured and fellow defender Erik Pieters should be fit despite having to come off in Sunday's FA Cup defeat at Chelsea, while Robert Huth (knee), Andy Wilkinson (heel) and Matthew Etherington (calf) are set to remain sidelined.
It will be interesting to see if and how Guidetti features after he was quoted by Swedish newspaper Expressen as saying there will be "a problem" if he is not selected for the game.
The Sweden international has so far made one appearance for Stoke, as a substitute, and he was left on the bench for the duration of the Chelsea contest, a match he had felt unwell in the build-up to.
Hughes said on Tuesday: "John is another one who is in our thoughts, so we will take stock of one or two things between now and the game and then make a decision."