The 22-year-old forward, who has already collected five senior international caps with Argentina, has agreed a five-and-a-half-year deal.
Director of Football Txiki Begiristain believes City have signed a player with significant potential.
“Julian is a player we have monitored for some time,” Begiristain said. “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 senior River Plate debut in October 2018 and has already forged a reputation as one of the best young forwards in Argentina.
He managed 36 goals and 25 assists in 96 River Plate appearances – including a strike in their 4-0 win over Racing in November, a result that sealed the Argentine league title.
Alvarez made his senior international debut in a World Cup qualifier against Chile in June last year, replacing Angel Di Maria with an hour gone, and was part of the squad that won the Copa America in July.
He will remain with River on loan at least until July 2022.
Everyone at Manchester City is looking forward to welcoming Julián to the club and we wish him the best of luck in his remaining time with River.