Alvarez joins City for a fee of €17 million but will stay at River Plate until at least the summer.
The 22-year-old forward, who has been capped six times by Argentina, has signed a five-a-half-year deal at the Etihad Stadium.
“Julian is a player we have monitored for some time,” City director of football Txiki Begiristain said in a statement.
“He is capable of operating in a number of attacking roles, and we firmly believe he’s one of the best young attacking players in South America.
“I am so happy we have managed to bring him to Manchester City. I really believe we can provide him with the right conditions to fulfil his potential and become a top player.”
Alvarez made his River Plate debut in October 2018 and has scored 36 goals in 96 appearances.
He made his senior debut for Argentina against Chile in June 2021.