The England midfielder completed a late deadline day loan to Everton on Monday evening after negotiations over the payment of his wages were finally thrashed out.
The former Aston Villa man’s City contract also expires at the end of the season, meaning there is an option to sign him permanently on a free transfer should the move go well.
Speaking to the media the day after signing on, Barry revealed that he was looking forward to working under new boss Roberto Martinez.
"The way I've seen his teams play over the years as soon as he got his first management job in English football he's always tried to play the right style of football.
"When I've played against his teams it's always been interesting to see what formations he's played.
"He's made it difficult for the teams playing against him and the way he had plans to fit me into the squad was very encouraging - the manager had a big part to play.
"I've enjoyed coming to Goodison Park and playing in great atmospheres.
"The fans here are fantastic and they always make it tough for opposing teams so it will be great to be playing on their side."
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