Atletico Madrid striker Griezmann is currently being chased by the Nou Camp giants.
Barcelona want to trigger his £87.5m release clause, which will come into effect on July 1.
Barca have previously denied an approach for the France international but in recent weeks have conceded that they are eyeing him up.
But in a sensational revelation on Movistar+, Griezmann revealed he is going nowhere.
He said simply: “I have decided to stay.”
Griezmann released a video on his Twitter feed immediately after the revelation, confirming he will remain at the Wanda Metropolitano.
Atletico Madrid have battled for over a year to keep their star striker.
Last year he infamously said there was a “six in 10 chance” of him joining Manchester United.
That move never materialised – in part because Zlatan Ibrahimovic’s knee injury meant Jose Mourinho was forced to change his transfer plans and sign a target man in Romelu Lukaku instead.
Griezmann has been dogged by speculation over his future all season and in January Atletico publicly threatened to complain to La Liga about Barcelona’s alleged approach.
It led to Barca publicly backing off from the player, although in reality they maintained their interest.
The retention of Griezmann is something of a coup for Atletico, who are seen as the third biggest side in Spain behind rivals Barcelona and Real Madrid.
Manager Diego Simeone is likely to see the Frenchman’s pledge to remain as a chance to go for the La Liga title next term, while also challenging in the Champions League.