The Nigerian was so convinced that he had sealed a move to the league strugglers that he drove to London before the window shut last Thursday and gave a television interview in which he referred to QPR as "we".
Albion later said he had not been given permission to speak to QPR and no deal had been reached.
"This has been an extremely difficult time for the club and it was imperative that we dealt with such a serious matter both fully and correctly," Albion chairman Jeremy Peace said in a statement on the club's website.
"We have made our position very clear throughout - both privately to Peter and publicly.
"Peter has apologised for his conduct to me personally and the club and our supporters as a whole."
Albion said Odemwingie, who has scored five league goals this season, had resumed full training and was available for selection for Monday's away trip to Liverpool.
Odemwingie, in the same statement, apologised for his actions.
"I understand how my actions have been viewed and want to apologise to the club and our supporters for any distress I have caused," he said.
"I want to reassure everyone at the club and our fans that I will continue to give my all whenever I am selected."
