The 28-year-old Griezmann has a contract until 2023 with Atletico, but has a buy out clause of 120million euros ($134million) and has been the target of several approaches from La Liga rivals Barcelona.
"Antoine Griezmann has told the club he will not continue as a Rojiblanco (red and white, the club's colours) next season," the club said on Twitter.
Within a few moments the player himself then posted a video explaining himself.
"After speaking with Cholo (club coach Diego Simeone), then with Miguel Angel and the people in the hierarchy of the club I wanted to speak with you, the fans, who have always given me a lot of love," said Griezmann, wearing a plain black t-shirt with a simple white background behind him.
"I wanted to tell you I have taken the decision to leave," said the French 2018 World Cup winner.
"The truth is it has been difficult to take this route but it is what I feel I need and I would like to thank all of you for the love you have shown me during these five years."