Griezmann, 28, is expected to arrive in Barcelona over the weekend, where he will pen a five-year contract with the Spanish champions before joining preseason training next week.
Griezmann will become Barcelona's third signing of the summer, following Frenkie de Jong and Neto.
Ernesto Valverde is desperate to acquire Griezmann's services before Monday, when Barcelona's first-team are due back for pre-season.
The Catalans were waiting to pounce on Griezmann after July 1 when his release clause dropped from £180million (€200m) to £107m (€120m). Once the release clause is paid, Barca is free to sign Griezmann.
After Barca president Josep Maria Bartomeu confirmed the meeting had taken place, the Rojiblancos released a strongly worded statement criticising both Barca and Griezmann's actions.
The drama may not end here, however.
"The player will sign a contract with his new club for the next five seasons, through to 30 June 2024, with a buyout clause of 800 million euros".
Barca are also said to be closing in on a deal for Atletico Madrid superstar Griezmann, and will also reportedly go after their former Brazil forward Neymar, who is believed to be desperate to leave Paris Saint-Germain.
French World Cup victor Griezmann was strongly linked with Barcelona last summer before he made the decision to stay at Atletico Madrid and also sign a new contract at the new Wanda Metropolitano Stadium.