The 28-year-old confirmed his intentions to leave Atletico last month, and Martin confirmed to Spanish radio station Radio Estadio on Wednesday that the Frenchman will head to the Nou Camp.
He said: "I am very clear about where he is going to play, it is known since March, at Barcelona."
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Griezmann helped France respond to their surprise 2-0 defeat to Turkey last weekend by featuring in their 4-0 victory over Andorra on Tuesday night.
The former Real Sociedad forward, who joined Atletico in 2014 after his £24million buy-out clause was met, was coy on his future in the aftermath of the Euro 2020 Qualifier.
He said: "There's a need for patience, as it's still soon. As I said, I know where I want to go. I want my future to be decided more than anyone, but there's a need to wait.
"I don't know if I'll remain in Spain. Maybe in two weeks we'll know something."
Griezmann, who has scored 133 goals in 257 games for Atleti, was close to joining Barcelona last summer before revealing he would stay on television.
But 12 months later, he is set to depart after his £107m release clause was met by Barca.
The move by the La Liga champions would represent an emphatic response to Real Madrid's summer spending spree, which rose to over £300m after the arrivals of Luka Jovic and Fernand Mendy this week.
Griezmann would form a devastating front three alongside Luis Suarez and Lionel Messi at the Nou Camp, with a first Champions League trophy since 2015 the clear priority for coach Ernesto Valverde.
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