Atletico also claimed that Griezmann had told the club that he had struck a deal with Barcelona in March, just days before the second leg of their Champions League last-16 tie with Juventus, which saw them dumped out by a Cristiano Ronaldo hat-trick after winning the first leg 2-0 in Madrid.
Griezmann joined Atletico in 2014 and has scored 133 goals in 257 appearances, lifting the Europa League in 2018.
He won the Golden Boot at Euro 2016 when France were beaten in the final on home soil by Portugal before helping to guide his team to World Cup triumph in Russia last year.
The sale of Griezmann comes after Atletico stumped up a whopping €126 million to sign rising star Joao Felix from Benfica last week, making the 19-year-old one of the five most expensive players in history.
The fee was a record paid by the capital club and the highest ever received by a Portuguese outfit, and the inevitable sale of Griezmann helps finance such a huge transfer for a young player.
Felix burst onto the scene last season, scoring 20 times and making 11 assists in all competitions for Benfica as they won the Primeira Liga and reached the quarter-finals of the Europa League.
On Friday, Atletico also unveiled Felix's former Benfica teammate Ivan Saponjic, the 20-year-old arriving after signing a three-year deal with the Spanish club.