The 17-year-old forward has drawn comparisons with Brazil and Paris Saint-Germain star Neymar and was also being courted by Liverpool, Shakhtar Donetsk and leading Spanish clubs.
But City have won the race to sign the wonderkid, who has scored twice in six first-team appearances for Fluminense in their state championship this year.
The Italian football journalist Fabrizio Romano reports that Kayky will arrive in Manchester next year and personal terms have been agreed for a five-year deal.
City will pay Fluminense an initial £8.5m with add-ons to follow which could take the eventual transfer fee to around £15m. The Brazilian club will also receive a percentage of any future sale.