The 29-year-old completed his switch to Goodison Park from Wigan Athletic for an undisclosed fee yesterday.
"I hope to be on target as frequently as possible here," Kone told the club's official website. "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. Playing for Everton is moving to another level, a slightly higher standard compared to Wigan and so I hope to be on my best form.
"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."
The Toffees, who are under the new leadership of Roberto Martinez, finished sixth in the Premier League last season.