The season Barry had under manager Roberto Martinez convinced him Everton was his long-term destination despite there being interest from elsewhere.
"Last season certainly helped me in terms of making my decision," he said.
"My mind never really went away from signing for Everton.
"I had a conversation with the manager at the end of the season and he told me he wanted me to sign.
"My agent did get a few calls from some other teams so then your mind can wander but nothing really took me away from being at Everton.
"I had a conversation with the chairman (Bill Kenwright) and manager after coming back from holiday and the contract was agreed.
"You could tell from my football last year I was playing with a lot of confidence.
"He (Martinez) is keen for players to learn and I thought I learned a lot from him last season - even with my experience.
"He was a big reason why I wanted to come back. The way the manager speaks to me I can play into my 40s!"
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