The Ivorian played his 35th match for the Toffees on Sunday, which activated the clause in his contracting entitling him to stay another season at Goodison Park
Kone also scored a hat-trick in the 6-2 win over Sunderland.
"It's almost a sense of relief more than anything," Kone said.
"I really wanted to stay beyond this season and now that wish has come true.
"It's come at a great time for me and means that I can concentrate fully on my game to try and make sure it turns into a happy season for us."