The Brazilian winger spent last season on-loan with Girona, another club owned by City's umbrella company City Football Group, helping them qualify for the Champions League.
He joins City for €40m, signing a deal to 2029.
"I am very happy and proud of myself and of my family who are out there, for helping me get here,” Savinho told City's website.
“I have to thank God as well for giving me this opportunity to be here at Manchester City. I am very happy, I still can’t believe I’m here, but with time, it will sink in.
“What I am experiencing here, I just arrived and I turned to my representative and my stepfather and said that it would be impossible to turn down Manchester City.
“And they were showing me what the training centre was like, what the club’s structure was like.”
Savinho will wear the number 26 shirt and also said: “It’s a joyful game, it’s a game that I usually say is a true game, a beautiful game.
“And I want to start training to adapt to Manchester City’s football.
“I think that since I was little, since I was at Atletico Mineiro, I watched Manchester City games.
“I have a friend whose dream was for me to become a Manchester City player.
“We used to play video games together, and he always played as Manchester City. I played with other teams, and he said that his dream was for me to one day join Manchester City and that I had the potential to get there.”