The Ivory Coast international reunites with former Latics boss Roberto Martinez, who signed Kone from La Liga outfit Levante last summer.
The 29-year-old scored 11 league goals in his maiden season in the Premier League, and contributed five assists, in a campaign that ultimately ended in relegation.
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But Kone has opted to follow Martinez to Goodison Park following Wigan's descent to the Championship, and the Spanish boss believes his new forward is at his peak.
“Arouna had a big injury to his cruciate and missed one-and-a-half years. That can sometimes be negative, but in his case it was the opposite,” said Martinez last week.
“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.”