"The 58-times capped Argentina global has informed the club he will move to pastures new, but leave behind many happy memories", City said in a statement on Saturday.
According to Dimitri Seluk, Toure would find it hard to turn down a new City deal if he was offered one, but the midfielder will have a long list of clubs to choose from in the summer.
"It's a huge result for us", said Swansea manager Paul Clement.
"I read a lot of stories about a new City contract but I know nothing about this".
"Maybe it is the first time I announce it but they have to come to support more than ever and to to express gratitude for one of the most important players in the history of Manchester City". I remember at that time [Sir Alex] Ferguson called us the "noisy neighbours" and this is something that I have made sure I have been since that time!
"It's one of those debates that as players we'd love to get involved in but we're not allowed to so that's what makes it very frustrating as they aren't willing to listen".
Zabaleta arrived at City from Espanyol in August 2008, a day before the Abu Dhabi takeover transformed the fortunes of the club.
The scores remained the same after Mahrez's disallowed penalty, allowing Manchester City to tighten their grip on a Champions League place finish. That is his only focus.
Senior City sources said there is a "strong chance" he will be offered a contract extension.
"As a player you are happy to play games on the field and this is something you enjoy the most, but if you really care about the club, you feel something inside of you that you want to create something big and that was one of the main things for me".
Toure has been linked with clubs in Italy and China as well as Crystal Palace, West Ham United, Newcastle United and Brighton.
City climbed two points above Liverpool, which dropped to fourth place ahead of its match away to West Ham on Sunday, in the race for a top-four finish and qualification for next season's Champions League.