Martinez will lose Kone next month to Ivory Coast's African Nations Cup campaign.
He said: "He has been a joy to work with. I have never seen a foreign player arrive in England and adapt so quickly.
"He has incredible finishing ability and technical quality.
"Arouna had a long period when he wasn't involved with the national team, and that was hard because he loves representing his country. When he is happy, we are happy, and I am very pleased he is back in their squad."