Savinho shone last season on loan at Girona, another club owned by the City Football Group (CFG).
City will reportedly pay a fee of 40 million euros (31m, $44 million) for the 20-year-old, who has signed a five-year contract.
Despite being registered to the Ligue 2 club, Savinho never played a minute of action for Troyes.
After his signing from Atletico Mineiro in 2022, he was immediately loaned to PSV Eindhoven.
The Brazilian international then spent the last 12 months in La Liga, where he scored nine goals and provided 10 assists as Girona finished third behind Real Madrid and Barcelona to qualify for the Champions League for the first time in their history.
