The 27-year old, who scored the winning goal against Marseille in the Europa League final last month, announced his decision in a documentary broadcast programme called "The Decision", made by Spanish network Movistar Plus.
Griezmann will now focus fully on France's World Cup Group C campaign which starts on Saturday against Australia.
Speaking to Spanish radio station RAC1 Messi said, 'It's obvious that I like him [Griezmann].
The concept behind Griezmann the video comes from LeBron James' "The Decision" from 2010, where he revealed publicly that he would join the Miami Heat.
Griezmann has been a long-term target for Atletico's La Liga rivals Barcelona and the French global was strongly tipped to make the move to the Nou Camp this summer.
After months of speculation, Antoine Griezmann has finally come to a decision on his club future.
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"They are doing everything possible to make sure the team keeps growing".
Griezmann looked likely to be swayed by ongoing interest from Barca, with the LaLiga champions' president Josep Maria Bartomeu in May revealing he had spoken with the player's agent.
"I feel there are things to do with Atletico", Griezmann added.
"I do not have anything clear, if I'm going to leave or I'm going to stay", he said in the show.
His words appeared to have the desired effect, with Atletico striking an agreement for Monaco star - and compatriot - Thomas Lemar, while Djibril Sidibe is also expected to move to Madrid.
The La Liga champions will now have to adjust their summer transfer strategy, though, following Griezmann's decision to snub them in favour of remaining at Atletico.