Spanish reports say Atletico will pay 75 million euros for the forward, with potentially 10 million more in bonuses.
The 24-year-old arrived at City for just £14 million (16 million euros) in January 2022 from River Plate, winning two Premier League trophies and the Champions League among other silverware.
Alvarez also helped Argentina lift the World Cup trophy in December 2022 and the Copa America in 2021 and 2024.
“Today I say goodbye to this amazing club, with a lot of emotion,” Alvarez told City’s club website.
“These have been two very special years. During this time, I have grown and learnt a lot — both as a player and as a person.”
Alvarez scored 36 goals for City in 103 appearances across all competitions.
“He’s incredibly loved by the team for his behaviour but like I said many times for many players, he wants to leave and have a new challenge,” said Manchester City coach Pep Guardiola last week.
Diego Simeone’s Atletico have also signed Robin Le Normand and Alexander Sorloth as they reinforce heavily to compete with Real Madrid and Barcelona, following a disappointing fourth-place La Liga finish last season.
Atletico begin the new campaign with a visit to face Villarreal on August 19.
© Agence France-Presse
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