The fee is made up of an initial £64.4m (75m euros) with a further £17.1m (20m euros) in potential add-ons.
It would be a record sale for City, surpassing the £50m Chelsea paid for Raheem Sterling in 2022.
Alvarez said he would wait until Argentina’s involvement in the 2024 Olympics football ended before making a decision on his future.
The team were knocked out by hosts France last Friday.
Manager Pep Guardiola had been keen to keep the 24-year-old and the Spaniard said earlier in August that he “counted” on Alvarez ahead of the start of the season.
“I count on him, but he said in the news that decisions will be made all together,” said Guardiola.
But, as has been the case in the past with Ilkay Gundogan, Riyad Mahrez and Aymeric Laporte, City will not stand in the way of a player who wants to leave.
Atletico, who have also agreed a deal to sign Chelsea midfielder Conor Gallagher, are yet to agree personal terms with Alvarez.
The Argentine, who joined City in 2022 in a £14.1m deal from River Plate, has scored 36 goals in 106 appearances for Guardiola’s side.
Alvarez won the Treble during his first season at the Etihad and the striker featured during Argentina’s 2022 World Cup victory in Qatar midway through the campaign.
Alvarez’s status at Manchester City was going to be an issue from the moment he won the World Cup with Argentina in 2022.
Having arrived from River Plate as an unknown for a relatively small fee earlier in the year, Alvarez had made 20 City appearances – but fewer than half were as a starter.
The reality was that he would never displace Erling Haaland as a number nine, so he would have to either compete with the likes of Phil Foden, Jack Grealish, Jeremy Doku, Bernardo Silva and others for a wide berth, or accept a role as back-up.
And his enhanced status meant the latter option was not going to work in the long term.
Atletico are a huge club with Champions League aspirations and are an attractive alternative.
For City, it could mean a greater involvement for 20-year-old Brazilian new boy Savinho than was initially expected following his £30.8m arrival from Troyes.
It could also nudge manager Guardiola to reinforce a squad that is looking to win the Premier League title for an unprecedented fifth successive season.
