"Most likely I will join on Tuesday. I've already signed a contract. The parties have been left to negotiate among themselves and then my dream of playing in the English Premier League will come true.
"I returned from England on Sunday morning after signing a personal contract with the club.It's now left for both clubs to negotiate then I will achieve my dream of playing in England.”
The forward says he turned down a move Greek club Panathinaikos.
''The first proposal was received last year. But then I saw no point in moving from the Russian championship to Greece.
"In addition, I hoped that Lokomotiv would qualify for the Champions League. But we did not. So I opted for West Brom because I have always wanted to play in the English league.
"But I want to thank Panathinaikos for their interest in me. They are a great club.''
Odemwingie had been offered to Tottenham as part of Lokomotiv's failed bid for Roman Pavlyuchenko, but says he was unaware of that particular deal.
''I read in the newspapers of the possible transfer of Pavlyuchenko. But nobody told me of the Tottenham situation.''
Odemwingie has previously played for Belgium's La Louviere and French club OSC Lille.
He follows in the footsteps of Ifeanyi Udeze and Nwankwo Kanu, two other Nigerians to suit up for the Baggies.