Julian Alvarez joined City on his 22nd birthday.
The Argentinian forward has already collected five senior international caps for his country, agreed a five-and-a-half-year deal in January 2022.
He will remain with River Plate on loan until the summer of 2022.
Director of Football Txiki Begiristain believes City have signed a player with significant potential.
“Julián 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.”
Álvarez 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 has managed 36 goals and 25 assists in 96 River Plate appearances to date – including a strike in their 4-0 win over Racing in November, a result that sealed the Argentine league title.
Álvarez 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.
Having linked up with the City squad in the summer of 2022, Julian has made a fine start to his Etihad career, impressing both with his predatory instinct in front of goal along with his awareness and vision.
And the 22-year-old was also part of the successful Argentina squad which tasted glory at the 2022 World Cup finals in Qatar.
Alvarez enjoyed a superb tournament, scoring four goals in total, including a brace in the semi-final against Croatia.
He then started in the final to help his country be crowned world champions for a third time as Argentina beat France 4-2 on penalties after a dramatic 3-3 draw over 120 minutes.