West Brom boss Steve Clarke was hoping to keep the Nigeria international at the Hawthorns and he rejected two bids from his QPR counterpart Harry Redknapp.
Odemwingie was upset by Clarke's refusal to budge, taking to Twitter earlier this week to vent his frustration.
But the Baggies appear to have accepted that Odemwingie wants to go and he arrived at Rangers on Friday to complete the deal insisting that he will depart West Brom on good terms.
"Of course I love West Brom and I always will. But I'm very optimistic that I will join QPR, it's a new chapter in my life," he told Sky Sports News.
"I am optimistic. A few good players have arrived here (at QPR) and I am happy with the trust Harry Redknapp has in me.
"The last few results have given us a chance to stay up. I don't think the owners will bring in so many players if they don't think it will happen.
"It's not 100 per cent (the deal), it's not sorted yet but I hope West Brom will be happy with what they get. And of course they are hoping to get players themselves.
"I just hope things will go well in the next few hours."
Asked about his Twitter comments, he said: "I had to push a little bit!"
Redknapp admitted he is hopeful of securing Odemwingie, plus Spurs duo Jermaine Jenas and Andros Townsend on loan.
"Peter Odemwingie has pace, great movement," Redknapp said. "I like him and is a player that has always given us problems when I was at Tottenham.
"I think if we can get Odemwingie he would be a great signing for us, but whether we can pull it off I am not sure."
On Jenas and Townsend he told London Call-In: "I managed the pair of them at Tottenham and JJ is a midfield player who can get from box-to-box.
"He is a good player, played for England, good lad and has a good attitude. I think he will be a good player for us.
"And Andros Townsend I think is a kid with a fantastic future. I like Andros an awful lot. He is a strong, quick, brave winger."