Having signed a five-year contract extension only last summer, the French forward made the shock statement on Tuesday evening via Atlético's official social media channels after meeting with Diego Simeone - the team's manager - and the chief executive, Miguel Ángel.
Griezmann had previously been attached with moves to Barcelona and Manchester United.
According to Cadena SER, via Mundo Deportivo, just a year after announcing he was to turn down Barcelona advances to stay with Atletico, the World Cup victor now looks to be edging closer to a switch.
"Thanks for everything, from the bottom of my heart", Griezmann said.More news: Hotel Guests Found Dead, Impaled by Crossbow Bolts
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Griezmann said in a video posted on the club's Twitter account: "It has been five incredible years, thank you very much for everything, I carry you in my heart".
He said: "Barcelona are now ready to pay €125M release clause for Antoine Griezmann".
The Frenchman has scored 133 goals in 256 appearances for Atletico since joining from fellow Spanish outfit Real Sociedad in 2014.
"I wanted to tell you I have taken the decision to leave", said the French 2018 World Cup victor. "I believe that is what I need".
"I have enjoyed a lot, I have left everything in the field, I have tried to behave well, I have tried to give joy to the people who have come to the Metropolitano and also away from home, and I only have gratitude for all of you".