The 32-year-old completed a £2.25m switch to the Bluebirds, seven months after trying to force a move to Queens Park Rangers.
"The Cardiff fans have been great," Odemwingie told reporters. "People I've met have welcomed me and I know the great atmosphere they create.
"I told my wife yesterday that what I see in this squad is stronger than West Brom. It doesn't surprise me the success they've had under Malky Mackay, I've really enjoyed his training so far.
"I feel like I'm starting over now. Every goal or even assist for me now for Cardiff will mean everything to me. I am starting from zero. Every performance I want to score. The earlier I get a goal the better after not scoring for six months."
The Nigerian could make his debut against Hull City at the KC Stadium this afternoon.