Odemwingie spent the past seven months in the wilderness at West Brom after the debacle of his aborted move to QPR before Mackay bagged the 32-year-old for around £2.5million.
Mackay said: "He has guile, a great touch, awareness. I know exactly what I have got: an intelligent, articulate lad who had a smile on his face since the day that he got here.
"He is in the need of match fitness and training and we need to blend him in gently.
"But we have an exciting talent for what I believe is a really fantastic price."