The centre-back finalised his switch to Goodison Park earlier this month in a £30m transfer, turning down interest from a number of other clubs - ex-employers Manchester United among them - in the process.
Keane was rewarded for his impressive form at Burnley last season with a couple of England caps and, heading into what is a World Cup year, he is targeting more regular playing time on the international stage.
"I thought Everton was a club that was going in the right direction and one that I can fit into really well," Sky Sports News quotes him as saying.
"I feel like it's the right time for me to come to this type of club where I'll be taking another step into the Europa League, which I've never played before.
"I want to try and push on some so I can force myself into the England team. First of all I need to keep myself in the squad, keep fit and playing games here at Everton and playing well - that's my main focus.
"In the back of my mind I've always got England and the World Cup in the summer. I know if I can impress, I'll put myself in the manager's thoughts and hopefully I can do that."
Keane spent two years at Burnley after joining from Man United, where he failed to make the first-team grade upon graduating from the academy.