The former Liverpool and England goalkeeper will provide cover for first-choice Ederson and second reserve Claudio Bravo over the course of the forthcoming season.
City were widely linked with Asier Riesgo, the veteran Spanish goalkeeper currently without a club, but his arrival would have used up one of the 17 spaces available for non-homegrown players in Premier League squads.
With City likely to fill all 17 spaces following the arrivals of Rodri and Joao Cancelo, a homegrown goalkeeper who would be satisfied with a largely non-playing role was needed.
The 33-year-old Carson fits the bill and is likely to be one of five homegrown players included in City's final Premier League squad, alongside John Stones, Kyle Walker, Raheem Sterling and Angelino, a fellow new signing.
How could Manchester City line up this season?
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Angelino, a Spain Under-21 international who re-joined City from PSV Eindhoven this summer, qualifies for homegrown status as he spent three years of his career in England with City before turning 21.
Players who are currently aged under 21 are not required to be registered as part of Premier League squads, meaning that 19-year-old Phil Foden does not yet count towards City's homegrown quota.
Carson made 33 appearances for Derby last season under Frank Lampard before losing his place to understudy Kelle Roos, who has been retained as first-choice by Lampard's replacement Phillip Cocu.
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