His final game was the 6-0 thumping of Watford in Saturday’s FA Cup final.
An announcement regarding the 33-year-old’s next move will be imminent.
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“He defines the essence of the club. For a decade he has been the lifeblood, the soul, and beating heart of a supremely talented squad.
“A booming voice in the dressing room yet a quiet and measured ambassador off it, Vincent can be as proud of himself as we are of him.
“I am not sure he expected to lift the Premier League trophy on four occasions during his captaincy but he will be remembered and revered whenever this period of unprecedented City success is spoken about by future generations.
“His leadership, intelligence and determination have seen him adapt brilliantly to playing under four different managers and overcome some debilitating injuries. He is a special character who has answered every demand the club has made of him.
“We now look forward to celebrating his testimonial match in September so that we can properly celebrate his City contribution. He will always be part of the City family.”
Kompany wrote an open letter to City supporters. It read: “Dear all,
“Community Shield Winners! Back 2 back League Cup Winners! Back 2 back Champions of England! FA Cup Winners!
“We’ve just seen the close of an incredible season. My 11th as a Blue. And I cannot believe I’m writing this but … also my last as a Blue. Countless of times have I imagined this day, after all, the end has felt nearby for so many years. It still doesn’t feel real. Man City has given me everything. I’ve tried to give back as much as I possibly could. How often does someone get the chance to end such an important chapter, representing a club with such great history and tradition, in such a great fashion?
“The time has come for me to go now.
“As overwhelming as it is, I feel nothing but gratefulness. I am grateful to all those who supported me on a special journey, at a very special club. I remember the first day, as clear as I see the last. I remember the boundless kindness I received from the people of Manchester.
“I will never forget how all Man City supporters remained loyal to me in good times and especially bad times. Against the odds you have always backed me and inspired me to never give up.”