The 33-year-old was deemed surplus to requirements at Manchester City and was offered the chance to join the Toffees on a season-long loan deal, and Barry has admitted that his discussions with Martinez reassured him about his role.
Barry told The People: "It was how relaxed he was about everything. How he made me feel about my own game, what he thought of me, what he said I could achieve this season. It's easy for a manager to say those things but, sitting there and listening to him, I believed in everything he said.
"I'd seen the style of his teams and the way they played. I knew this was his first season at Everton, so it was a bit of a gamble.You weren't sure how the fans were going to take to him, how his style of play would work.
"Everton needed to change their style to fit the way Roberto wanted them to play, so you weren't sure how it was going to pan out. But the way he spoke to me, I believed in him and virtually every word he said to me has come true."
Everton face Arsenal at Goodison Park later today.