The Ivory Coast forward followed the Spaniard from Wigan to Everton on Monday for a reported fee of £6.5 million, signing a three-year deal.
The 29-year-old enjoyed a solid debut season in the Premier League, scoring 11 league goals, and is thrilled to have made the switch to Everton and link up with Martinez once again.
"I feel delighted. I'm really happy about joining this team," said Kone.
|14/1||Everton are 14/1 with Paddy Power to finish in the top four
"It's an honour to be back working with the manager once again. Last season he really helped me a lot.
"For my first season I did the absolute best I could, but I think that joining up with him [Martinez] at this club is like another dimension for me and I hope that I'm going to continue to improve alongside him.
"We'll keep working hard to try and help the club achieve all of its goals."
Everton have not won a major trophy since lifting the FA Cup in 1995 and, after winning the same competition with Wigan last season, Kone is aiming to fire the Merseyside club to silverware.
"I'm really eager to do my best to try and win something again this season," Kone continued.
"I really believe in this team and I think we will have a great campaign next season. I can't wait to make my debut for this club.
"I think that with the quality of squad Everton has, we will have a good season. I hope to score as many goals as I can next season."