The veteran goalkeeper moves to City on a season-long loan with the champions taking on his wages.
“It's an honour to have signed for City on loan," Carson said. “It's something I didn't expect but an opportunity I simply could not turn down. To be part of this squad – the Champions of England – is a dream come true.
“I can't wait to see Pep's work on the training field up close. What he has achieved in his management career has been amazing, and it's every player's dream to play under him.
“Hopefully, my experience will prove useful as we try and make it three Premier League titles in a row."
City chief Txiki Begiristain added: “We have strength in depth in the goalkeeping department, and the wealth of experience Scott will bring to the squad will be important as we once again look to compete on all fronts."