"The truth is it has been difficult to take this route but it is what I feel I need. I would like to thank all of you for the love you have shown me for these past five years," said the Frenchman in a video posted on social media.
Griezmann, 28, arrived at Atletico Madrid from Real Sociedad. He scored 133 goals in 256 appearances for the side and won the 2016 Spanish SuperCup and the 2018 Europa League. There were also two defeats in the Champions League final against Real Madrid.
Griezmann did not say where he would play next. However his next destination is rumoured to be Barcelona who tried to sign him just before the 2018 World Cup.
"Antoine Griezmann has told the club he will not continue next season," Atletico Madrid said on Twitter.
Griezmann's departure will force head coach Diego Simeone to restructure his squad. Lucas Hernandez has opted to leave for Bayern Munich and skipper Diego Godin has announced he will quit the club.
The Uruguayan, who was instrumental in convincing Griezmann to stay last summer, received an official farewell in his final home game for the club on Sunday.
“It isn’t easy for a player to receive so much love,” added Griezmann in his message to the fans. “I wanted to tell you so that you’re the first to know, after the coach and the club.
"I’ve given my all on the pitch, I’ve tried to behave well. Thank you so much, and goodbye.”