The 28-year-old will sign for Barcelona for five seasons after announcing on Atlético Madrid's twitter account that he had chose to leave the club.
Spanish newspaper Mundo Deportivo says the Catalans will pay Griezmann's release clause of €120 million (RM556 million) and the 28-year-old has signed a five-year deal at the Camp Nou.
"Atlético Madrid believes the termination of the contract occurred before the end of last season due to events, acts and demonstrations carried out by the player and that is why we've already started procedures considered appropriate to defend our rights and legitimate interests".
It's anticipated the representatives are paying the €120m clause to release Griezmann from his contract.
Atletico are furious they have been forced to accept the £108m bid and vowed to take legal action against Barcelona and the player.
Griezmann is the fourth French player in the current first-team squad behind Lenglet, Dembélé and Todibo.
He signed a new five-year deal in June 2018 but announced in May he would be leaving the club this summer.
The former Real Sociedad forward departs Atletico after five prolific seasons in the capital, which saw him score 133 goals as well as helping the club win the Europa League, UEFA Super Cup and Spanish Supercopa.