The Goodison Park faithful have voiced a slight concern that the reported £6.5 million transfer fee is too high for a player approaching his 30th birthday.
But Martinez is adamant that injuries have held back the 29-year-old and predicts his best years are yet to come.
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“It refreshed him and he is a young 29-year-old. He’s at the peak of his career.
“When you get a player where from the physical point of view, to the tactical and the technical he is in peak condition, it really excites you and that’s where Arouna is.
“He had a fantastic move from Holland to Seville for big, big money where he had a little bit of trouble with inconsistency and injuries, but now he is back to his very, very best and he will be a big asset.
“Everyone would understand that he brings something different to what we have at the football club at the moment.”
Kone shone for Wigan as they comprehensively beat Everton at Goodison Park during their successful FA Cup run last season and received a standing ovation from the Toffee fans - something Martinez thinks impressed the striker.
“I think he was impressed with Goodison Park,” the Spaniard added.
“His experience playing as an away player is something that gave him a great feeling and he was impressed – it was something that hasn’t happened to him too often.”
Kone’s arrival could cast doubt over Nikica Jelavic’s future at the Merseyside club after failing to live up to the success of his first season in England, but Martinez has dismissed such claims.
He continued: “At this stage of the season what I want is to have the strongest possible squad.
“I think we need four players – one per position –and that’s not looking at players or individuals at the moment, that’s just to start the work in pre-season, allow that competition that we need and then just to be aware that we need to go into every competition to win.
“When we go into the League Cup we expect to have a strong squad, the FA Cup the same and also the League. And that’s looking at the youngsters as well.
“I want to get the strongest possible squad.”