The Ivorian striker has managed just 22 appearances since following manager Roberto Martinez to the Toffees from Wigan in 2013 for ??6m.
He played six times in a debut season cut short in October by a knee ligament injury which sidelined him for almost 14 months.
However, the 31-year-old featured in 16 matches between December and the end of the last campaign and that has helped restore his confidence as he prepares for pre-season.
“In terms of my injury, last season really helped me to come back and get fitter,” he told evertonfc.com.
“When I left Wigan, I knew I was coming to a bigger club, a successful club, and I knew that being surrounded by such a great group of players could have a great impact on myself so to suffer the injury that I did was very difficult.
“I feel a lot better physically now. The few games that I was able to play last season allowed me to regain a lot of my confidence which is very important.
“Now it’s all about this summer and this pre-season and making sure I set out as I mean to go on.
“The fans haven’t been able to see me at my very best level but I hope I can get there next season and show them what I am about. I am hungry to do that and I want to prove I can cut it here.
“The fans and everyone around me have been really supportive and that’s kept me going throughout the difficult months and I really want to repay those people now and use my performances to help push the team towards the top of the table where it deserves to be.”