The 22-year-old signed for the Citizens in January for around £14.2m, penning a five-year contract, before returning to his native homeland on loan.
City have now announced that Alvarez will fly to Manchester this weekend ahead of the 2022-23 campaign and will be unveiled to supporters at a club event taking place on Sunday, alongside summer signings Erling Braut Haaland, Kalvin Phillips and Stefan Ortega.
Speaking to mancity.com on his arrival at the club, Alvarez said: "I am incredibly happy and I feel ready to play for City.
"This is, without doubt, one of the biggest teams in world football. You only have to see what this team has won in the last decade to understand the quality of the setup.
"I feel confident I can flourish here. The style of play [Pep Guardiola] encourages is exciting and I can't wait to be a part of it."
The Argentina international added: "City has an amazing recent history of Argentinian players and I want to put my stamp on the club in the same way Sergio Aguero, Pablo Zabaleta and Carlos Tevez did.
"I am so thankful for everything River Plate did for me and I want to thank the fans, staff and players for their support.
"But I am now 100% focused on Manchester City. I want to give my best to this club, help my teammates and contribute to Manchester City's success."
Alvarez, who will wear the number 19 shirt at the Etihad Stadium, is regarded as one of the brightest prospects in South America, and leaves River Plate after recording 53 goals and 31 assists in 120 senior games across all competitions.
The forward has been in sensational form in front of goal since the beginning of last year, netting 41 times in 69 games, including six strikes in an 8-1 victory over Alianza Lima at the end of May.
Alvarez is now set to join up with Guardiola's first-team squad for their pre-season tour of the USA later this month.