While on loan, he saved a penalty in a 4-3 Premier League win over Newcastle United in May 2021.
He came on as a late substitute in a Champions League last-16 second leg draw with Sporting Lisbon in March 2022.
City said in a statement: “During his time at City, Carson has been praised by goalkeeping coach Xabi Mancisidor and peers Ederson and Stefan Ortega Moreno for his work ethic and the effect of his positive attitude amongst the group.”
Last month former City team-mate Kyle Walker, who joined AC Milan on loan in January, said: “To come in every day knowing you’re the third-choice keeper -mentally, I have to take my hat off to him.
“He’s had a fantastic career but to still have the love for football and do what he does, these are the people you need around the place.”
Carson has played for 10 teams since making his Leeds United debut in 2004, including two years in Turkey with Bursaspor.
He won the Champions League and Super Cup with Liverpool, and two Premier Leagues, two Champions Leagues, an FA Cup, two League Cups, one Community Shield, two Super Cups and a Club World Cup with City.
