The Nigeria international turned up in west London, despite no agreement being in place between the two clubs and was refused entry into the Hoops' stadium by club officials.
Odemwingie has attacked West Brom's fans and club chiefs recently on Twitter, but will remain at the Hawthorns until the summer at the very least.
Baggies chairman Jeremy Peace told the club's official website: "This evening's developments have brought a conclusion to what has been an unsavory affair.
"As our sporting and technical director Richard Garlick has repeatedly said in recent days, we had no need or desire to sell our core players.
"The only way we would have considered letting Peter leave was if an acceptable offer was forthcoming and if we had found a suitable replacement at relatively short notice.
"Neither materialized and, in the end, the matter became a point of principle as much as anything.
"Peter has acted wholly unprofessionally. He must now accept the fact he remains under contract for a further 18 months and has to focus on his Albion commitments."