A statement on Atletico's website confirmed the clubs will work over the next few days to complete the transfer.
As the French national soccer team gears up for this week's World Cup, speculation continues to mount over the playing future of one of the team's star forwards, Antoine Griezmann.
The forward has been expected to confirm his future before the World Cup and said Saturday that was still the case.
On Tuesday Griezmann revealed he has made a decision regarding a potential summer transfer to Barcelona, but isn't ready to make that decision public.
But he finally appears to have secured his next challenge, with Atletico giving every indication they want to close the gap on LaLiga champions Barcelona next season by signing a highly rated attacker.
Last summer came his most recent extension, when he added another year to take him up to 2022.
France's Antoine Griezmann smiles as he answers journalists' questions.
France coach Didier Deschamps prohibits players from undergoing negotiations during tournaments, pushing Griezmann towards making a decision.
Griezmann is looking to cap another spectacular club season, in which he scored 29 goals in 49 games as Atletico finished runners-up in La Liga behind Barcelona and lifted the UEFA Europa League.
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