Hart brought his 12-year stint at City to an end on Tuesday when he completed a £3.5million move to Burnley on an initial two-year contract.
Khaldoon said: "Joe Hart's contribution to Manchester City cannot be overstated. His 12 years at the club has seen him produce some remarkable performances and heart-stopping saves that will live in the memory for a long time to come.
"His passion for and commitment to this club, evidenced by a remarkable tally of 348 appearances, means he will rightly be regarded as a City legend in perpetuity.
"I want to personally thank him for everything he has given to us over very many years and he leaves with Sheikh Mansour's and my heartfelt best wishes for the next step in his career. He will always be welcome at the club."