Kone has revealed Latics boss Martinez's devotion to stylish football helped make up his mind to move.
Kone told wiganlatics.co.uk: "I'm very happy to be here and I'm doubly happy because I know how hard the manager has had to fight to get me here.
"I'm impatient to get started with my new club. It's a great challenge for me. Roberto has told me about the philosophy of the club, how it's a family club.
"He is a young manager who is trying to build something special here.
"He told me how he likes his teams to play on the floor, which is a style that I'm used to in Spain, and these were words which really persuaded me to join."
Wigan begin their Barclays Premier League campaign on Sunday with a home game against Chelsea, and Kone is hoping to be involved.
He said: "It's up to the manager of course but I'm ready having done all of my pre-season with Levante.
"I feel great and I would love to be able to take part in such a big game.
"I'm going to give my all every time I put the shirt on this season and I'm sure we can make progress in the league.
"I really hope that the fans will be satisfied that I'm a player who gives everything."