The 35-year-old joined in 2019, initially on a one-year loan deal from Derby County.
That agreement was then extended for a further 12 months last summer, and he went on to make his City debut in a 4-3 win away at Newcastle in May.
With his contract at Derby now expired, he has signed for City on a free transfer.
Capped four times by England, Carson boasts a wealth of experience from his 17-year career and counts West Bromwich Albion, Liverpool and Turkish outfit Bursaspor amongst his former teams.
Before joining City on loan, the Whitehaven-born keeper had spent the previous four seasons at Pride Park where he made more than 150 appearances for the Rams.
“It’s a pleasure and a privilege to be part of the setup here at City,” Carson said.
“To be around Pep and his backroom staff is fantastic and I feel I have learnt so much since I joined in 2019.
“The lads made me feel at home straight away and I have loved every second of my two years here.
“To commit for another year was such an easy decision. I want to continue pushing the other goalkeepers we have here and I want to make sure my experience rubs off on them.”
Director of Football Txiki Begiristain added: “Scott brings a wealth of knowledge to the squad.
“He is a former international goalkeeper who has played in lots of big games during a long career.
“We know he is always ready to play, if we need to call upon him.
Everyone at City would like to congratulate Scott on signing his new deal.