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.
Odemwingie becomes Cardiff's eighth new signing since their promotion to the Premier League and will provide added firepower, having scored 30 goals in his three-year spell at the Hawthorns.
|2/1||Cardiff are 2/1 with BetVictor to be relegated
"Peter completed his medical on Monday afternoon and will link up with his new team-mates later this week."
Odemwingie had fallen out of favour at West Brom after he tried to force through a move to QPR in January, and he is pleased to have been given the chance to make a "fresh start" with the Premier League new boys.
"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."