Jones, 29, heads to Wales to join Ole Gunnar Solskjaer's Bluebirds after three and a half years with the Potters, while Odemwingie's unsuccessful time with Cardiff comes to an end after just half a season.
Stoke manager Mark 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."
Odemwingie, 32, has signed an 18-month contract at the Britannia Stadium and could make his debut tomorrow night at Sunderland.
Meanwhile, Jones is not available for Cardiff's trip to Manchester United tonight but could make his bow at home to Norwich City on Saturday.