The 32-year-old Nigeria international had found himself surplus to requirements at The Hawthorns after his now infamous drive to London in a bid to engineer a move to QPR at the end of the January transfer window.
His efforts ended in failure as West Brom refused to accept QPR's bid but he is now keen to make a new start at Cardiff City Stadium.
"I missed football and I am delighted to come to a fast-progressing team," he told Cardiff City Player.
"They have a young manager with a lot of ambition.
"He has done really well in a short period and I hope to help the team become better and I am grateful for the confidence they have shown in me.
"I am very motivated and ready for action. The last six months, coming on as a substitute for 10-15 minutes was not what made me happy and I am a better player when I am happy.
"I am very hungry and I will show the same attitude I had when I was scoring a lot of goals in games in the Premier League."
Odemwingie will use the international break to get acquainted with his new team-mates before their Premier League trip to face Hull on Saturday week, and he is also keen to experience the atmosphere at Cardiff City Stadium.
He said: "My father-in-law is a City fan and he says there is a fantastic atmosphere in the stadium and that is what I want. A lot of people have told me the fans are great here.