The 19-year-old underwent a medical yesterday at the City Football Academy and signed his contract, with the club now making it official.
Manchester City have signed Brazilian Under-20 worldwide of Douglas Luiz from Vasco Da Gama in a deal reportedly worth £10.7million.
City's director of football Txiki Begiristain said on the club's official website: "Douglas is an exciting player with great potential".
Douglas will immediately be loaned to one of City's partner clubs Girona FC, who have just been promoted to La Liga.
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Wenger thanked those fans for their support. "I guess it's pretty exciting", Redmayne said. I didn't play as much as I'd like to a year ago .
"The day has come to say "see you soon" to the family who welcomed me as a child, in search of a dream, and introduced me to the world", he said.
On Friday, City confirmed a deal to bring in defender Kyle Walker from Tottenham in a deal that could reach £50million.
Although he is apparently less likely to have the immediate first-team involvement of his compatriot Ederson, Douglas becomes the fifth Brazilian on the books at the Etihad Stadium, also joining Fernandinho, Fernando and Gabriel Jesus.