The 19-year-old Brazilian youth international has signed a four-and-a-half-year contract with the Premier League champions.
“I’m excited to join Manchester City, one of the biggest clubs in the world,” said the right-footed centre-back.
“Everyone has seen the amazing achievements in recent seasons and I want to make my mark as we seek more trophies.
“Working with Pep Guardiola is something every young player wants to do and I know he can help me to develop into the best player I can be.”
City's director of football, Txiki Begiristain, stated, "Vitor Reis is among the most talented young defenders globally, and we are thrilled to have secured his arrival."
“He is excellent on the ball and outstanding in the air — he has all the attributes needed to be one of the best.”
Reis becomes City’s second acquisition of the January transfer window, following the signing of Uzbekistan defender Abdukodir Khusanov.
The club is said to be pursuing Eintracht Frankfurt forward Omar Marmoush as the window approaches its conclusion.
This season, City’s efforts to defend their Premier League title have been hampered by a series of injuries, especially in the defensive line.
They currently sit in fifth place in the standings after securing a 6-0 victory against Ipswich on Sunday.