Goal reported in June that the club had enterered discussions with the player over increasing his £20,000-a-week deal after a stellar breakthrough season under Roberto Martinez.
Barkley scored six goals in 34 Premier League appearances to earn a call-up to Roy Hodgson's England squad for the World Cup and attract interest from Manchester United.
"He brings back the memories of the big legends and the big players that we've had at the football club, but saying that he's still a young man and his best years are still to come," Martinez told reporters.
Barkley added: "It didn't take any persuading. As soon as I got told about it I wanted to sign.
"Over the coming seasons we want to push on and hopefully get into the Champions League. We've got ambitions and goals.
When asked if he could imagine life away from Everton, Barkley said: "I never think about it."
He added: "I've always looked up to Wayne Rooney coming through at Everton and playing for England at a young age. It's a great club."
Barkley's new deal will reportedly see him earn more than three times his original salary after agreeing a £65,000-a-week offer running until 2018.