The Nigerian forward had been linked with moves to Swansea and Stoke during the transfer window but Malky Mackay has won the race for the 32-year-old, who has signed a two-year deal after the £2.5million move.
Odemwingie becomes Cardiff's eighth new signing since their promotion to the Premier League and will provide added firepower.
Odemwingie's future at the Hawthorns had been subject to speculation since the last transfer window when he tried to force a move to QPR.
"I'm delighted to complete my move to Cardiff City. I'm looking forward to this fresh start at a club that is really going places, a team that's progressing fast," Odemwingie told the club's website.
"My father-in-law is a City fan and he's told me what a great club this is. I'm looking forward to meeting up with the boys and then start preparing for the trip to Hull after the international break.
"I've seen a little bit of the city and I know that my wife and I will really enjoy living in Cardiff. I can't wait to get started - this move makes me very happy."
