In a farewell message on the club's website, the forward said, "It's been an incredible five years; Thank you very much for everything, I take you in the heart," Sky Sports reported.
Griezmann, 28, has been linked with a move to Atletico's La Liga rival Barcelona since last year, and speculation has only intensified since the Catalonian club was embarrassed by Liverpool in the Champions League semifinal.
Last summer, Griezmann released a half-hour long documentary on Spanish TV station Movistar to tell fans where his future would lie – Barcelona or Atletico.
Having recorded two endings – one which said he would stay, and another which said he would go – Griezmann revealed he would continue playing with Atletico.
Griezmann went on to lift the World Cup with France one month later, scoring four goals, including one in the 4-2 final win over Croatia.
Atletico will finish the season second in La Liga and without a trophy after blowing a 2-0 first-leg lead in the Champions League last 16 against Juventus, and losing to Girona in the same round of the Copa del Rey.
Griezmann joined from Real Sociedad in 2014. Last season he helped Atletico win the Europa League.