Both the player and his agent revealed on a busy transfer deadline day that a deal had been done, and the Bluebirds have announced that the striker has become their eighth signing of the summer.
Odemwingie completed a medical on Monday and is now waiting on Premier League ratification before opening a new chapter in his colourful career in south Wales.
Cardiff are delighted to have acquired the services of a proven goalscorer, with the 32-year-old having netted 30 top-flight goals in three seasons at The Hawthorns.
Odemwingie had been looking for a route out of West Brom for some time, having decided that he needed a 'fresh start', and he cannot wait to get going at an ambitious club determined to establish themselves among the elite.
He told Cardiff City Player: "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.
"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."
Odemwingie is Malky Mackay's eighth summer signing, joining fellow new recruits Andreas Cornelius, John Brayford, Simon Moore, Steven Caulker, Gary Medel, Maximiliano Amondarain and Kevin Theophile-Catherine.