Odemwingie will leave the Bluebirds for Stoke, while 29-year-old Jones will move in the opposite direction.
The switch will be completed once the players pass their respective medicals and agree personal terms.
"Stoke City can confirm it has reached an agreement with Cardiff City over a move for striker Peter Odemwingie that will see Kenwyne Jones head to South Wales in a player-exchange transfer," reads a statement on the Potters' official website.
"The deal is subject to both players passing medicals and agreeing personal terms but the Potters hope to conclude their move for the Nigerian international over the weekend."
Stoke are currently 14th in the Premier League, while Cardiff are at the foot of the table.