The Nigeria international will face his former employers for the first time since his close-season move to the Welsh outfit on transfer deadline day when the two sides compete at the Cardiff City Stadium on Saturday.
Odemwingie was met with a furious backlash at The Hawthorns after trying to engineer a last-gasp move to QPR on the final day of the January transfer window, an incident that left him largely isolated at the Midlands outfit.
But Mackay has hailed the 32-year-old's character and insists he has been nothing but a true professional at Cardiff.
"There was a lot of press around Peter at the time and he took a lot of pressure over it," he said. "But I can only speak about the lad I know and (I have) talked to people who had managed and coached him before we completed the signing. They were all glowing about Peter.
"If they hadn't talked about him in those terms it might have been a cause for concern, but he's an intelligent man who speaks four or five different languages, has been smiling since he came here, is really talented and desperately wants to do well here.
"He is a joy to work with and a really good signing for us. If he hadn't been the right sort of character we would not have signed him."
Cardiff's home encounter with Steve Clarke's men marks the first of five fixtures in 17 days.
Having failed to register a victory in their past five Premier League fixtures - including a 2-0 reverse at Crystal Palace last Saturday - Mackay is hopeful the busy schedule can work in his team's favour.
He added: "We were all disappointed with last weekend's result. But we quickly put it behind us and looked ahead to Saturday.
"West Brom have done well under Steve Clarke and have players that can hurt you. It's a test we're looking forward to.
"Every game is one we want to win. The festive period brings a lot of games but we'll treat all of them in the same way. We're used to frenetic periods of games - hopefully that's something that bodes well for us over the festive period."
