The Ivory Coast international has followed the Spaniard from Wigan after a fee, believed to be around £6.5million, was agreed last week.
Martinez is also trying to tie up the signature of Antolin Alcaraz, another of his former Latics players, who is a free agent after his contract expired.
Kone, 29, scored 13 goals for Wigan last season despite spending a month on international duty with the Ivory Coast at the Africa Nations Cup. Despite his contribution, the Latics failed to avoid relegation from the Premier League.
While his new Everton team-mates are heading off to Austria for pre-season this week Kone will not be joining them.
He will link up with the squad later this month as he is on extended leave having been on international duty at the end of last season.
"I feel delighted. I'm really happy about joining this team," said Kone.
"For me it is the fruition of work that has been going on for a month now. I'm really pleased to be here and I hope that everything goes well and I can have a great season for the club, just like I did last year with Wigan.
"For me 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 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.
"I hope to be on target as frequently as possible here. I have faith in my own ability but I hope that everything goes smoothly and that I can also steer clear of injuries.
"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. "
Kone admits he is taking a step up but has no concerns he will not be able to meet expectations.
He feels joining a squad with the sort of competitive element Everton's has will only help.
"I've played against them in the Premier League and in the FA Cup and it is like moving up a level," he added.
"Every player dreams of playing for a bigger club and coming here is a big step up for me.
"I hope to be able to fulfil all my dreams and get as far as I can through hard work.
"I want to give my very best for this team and help them to achieve all their targets this season.
"I really believe in this team and I think we will have a great campaign next season and I can't wait to make my debut for this club.
"I'm raring to go because when you join a club it's that desire to start working that first comes to mind.
"I'm ready and willing to get started and can't wait to meet up with my team-mates and the coaching staff.
"I really hope that all goes well because I'm really eager to do my best to try and win something again this season."