The Spanish club revealed that Griezmann informed club officials of his desire to depart the Rojiblancos after five years of service.
"Thank you Atleti, I’m going to start a new challenge," the French striker said in a video message on Atletico's Twitter feed.
Barcelona have reportedly opened contract negotiations with Griezmann following news that they are prepared to trigger the €125-million release clause to sign the French superstar, according to the Guardian's Fabrizio Romano.
It's understood that Griezmann and Barcelona officials will meet over the next couple of days to finalize a five-year contract.
Although the release clause in Griezmann's contract that he signed last summer is set at €200 million, that figure will drop significantly on July 1, according to Isaac Suarez of Marca. It's also believed that Griezmann's former club, Real Sociedad, will collect roughly €24 million based on the 20 percent sell-on fee agreed in their deal with Atletico Madrid in 2014.
Speculation over Girezmann's future at the Wanda Metropolitano has been relatively quiet this year compared to seasons in the past. He appeared to be on the verge of an exit last summer before signing a new contract until 2023 to end uncertainty about his future ahead of the World Cup in Russia.
After joining Atletico from Real Sociedad for €30 million, Griezmann developed into one of the game's top players and has finished third in Ballon d'Or voting in two of the last three years. He was also named La Liga's Best Player ahead of Lionel Messi and Cristiano Ronaldo in 2016.
He has scored 94 goals in 179 league appearances at Atletico Madrid.
Meanwhile, Atletico Madrid will be busy this summer attempting to fill voids left by Griezmann and other players such as Diego Godin and Lucas Hernandez - whose departures have already been confirmed. Defender Filipe Luis is also reportedly going to leave the club once the season ends.