Swansea and Stoke were also keen to sign him but the Bluebirds have beaten them to his signature.
The 32-year-old was granted a work permit by the Home Office earlier on Monday which paved the way for the transfer to go through.
Odemwingie almost left The Hawthorns in January and turned up outside Loftus Road as he looked to push through a move to QPR.
That transfer never materialised and instead he has found himself pushed towards the fringes of Steve Clarke's squad.
Despite that, Odemwingie still registered 10 goals in 25 appearances for the Baggies last season and Cardiff boss Malky Mackay will be hopeful he can reproduce his best form for them.
Segal admitted Odemwingie had no option but to leave The Hawthorns and confirmed he is looking forward to a fresh challenge in the Welsh capital.
"Everybody would realise there was no future for him at West Brom, so this is a new start," said Segal.
"He is very happy and very ambitious and they (Cardiff) have a great manager in Malky Mackay and when they spoke today, Peter became even more enthusiastic."
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."