The 32-year-old was expected to leave West Bromwich Albion after falling out of favour due to his failed attempt to sign for Queens Park Rangers in January.
Despite receiving an influx of offers, Odemwingie has stated that Cardiff was the "right move" for him.
"Early in the summer there was bids from Fulham and West Ham, that was turned down," Odemwingie said in a press conference. "A club from Dubai came in. Last week I think Stoke City and Swansea City [made bids]. It was a collective effort to make a decision."
Odemwingie secured his exit from The Hawthorns on deadline day.