Odemwingie, who left West Brom for Cardiff City on the same day, had endured a negative relationship with the club since January when he was refused permission to discuss terms with Queens Park Rangers.
However, Anichebe has revealed that the animosity did not stop his fellow Nigerian from having positive things to say about his time with the Black Country outfit.
"I've spoken to Peter in the past and, no matter what people say about him, he has always had good words to say about the club," the Express & Star quotes Anichebe as saying. "He has always said what a good club it is – a family club. Hopefully I can help the club by playing well for them and I'm happy to be here."
Anichebe is thought to have cost the Baggies £6m.