Griezmann announced in May that he would be leaving Atletico this summer, but it was not until July, when his release clause dipped, that Barca confirmed they wanted to sign him.
"Atletico de Madrid believes that the termination of the contract occurred before the end of last season due to events, acts and demonstrations carried out by the player".
"The player will sign a contract with his new club for the next five seasons, through to June 30, 2024, with a buyout clause of 800 million euros", Barca said in a statement.
It remains to be seen how far Atletico will take their action against Barcelona over the Griezmann transfers, with talks between the club expected take place to try and resolve the dispute.
The Frenchman scored 133 goals in all competitions for Atleti.
Atletico Madrid's World Cup victor Antoine Griezmann is nearing a transfer to Barcelona, according to reports on Thursday in his native France and in Spain.
Atletico finished second in La Liga last season, nine points behind Griezmann's new club.
Barcelona will begin its summer tour on July 23 with five games in three different continents in a span of 19 days where it will play Chelsea, Vissel Kobe, Arsenal and Napoli twice.
Griezmann, who has won 72 caps for his country, moved to Atletico from Real Sociedad in 2014 and helped the club win the Europa League in 2018, scoring twice in the final against Marseille.