Odemwingie was booed when he appeared as a late substitute against visiting Sunderland a fortnight ago.
It was his first appearance since his Twitter rants against the club during January after a transfer request was rejected and hopes of a move to QPR were dashed.
But he received a warm reception from the Baggies followers who travelled to Stamford Bridge last weekend.
Odemwingie's chances of starting have increased, with Shane Long doubtful after aggravating an ankle injury.
Clarke said: "Everyone knows the Peter incident happened but it's past for us and we have all moved on from it, and I look forward to his contribution for the rest of the season.
"Peter and I have a good relationship, coach-player excellent relationship.
"I think he is a good talent and I look forward to him making a good contribution for the rest of the season."
Clarke added: "People have to move on. We have moved on from it and the less we talk about it the more likely we are to move on completely from it.
"Am I keen to see home fans put things in the past? I would like to think so and if he plays and scores goals they will give him a good reception."