City have enjoyed an unprecedented period of success since 2019, claiming four Premier League titles as well as the Treble two years ago, but finished last season without a major trophy.
Commercially, the two parties have achieved club record sales globally, according to City.
City Football Group (CFG) chief executive Ferran Soriano said: “We joined forces with Puma with the ambition to challenge ourselves and go beyond the expectations. We have achieved this and more over the last six seasons.
“Puma have seamlessly integrated into our organisation, and we have enjoyed many historic moments together, engaging fans globally.”