Manchester United had made Griezmann one of their top transfer targets this summer as they looked to add more attacking power to the squad.
And the France international had dropped clear hints over his willingness to move to Old Trafford.
But following FIFA's decision to uphold Atletico's ban on signing players, Griezmann revealed he was now ready to stay at the club.
And the 26-year-old has told French television show Telefoot that leaving Atletico after their transfer ban would be a "dirty move".
What Antoine Griezmann has said about his future Sun, June 4, 2017
What has Manchester United target Antoine Griezmann said about his future?
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Speaking to French broadcaster Telefoot in June…
It would be a dirty move to leave now
He said: "The ruling of the CAS has come through. Atletico cannot recruit. With my sporting advisor, Eric Olhats, we decided to stay.
"It's a hard time for the club. It would be a dirty move to leave now.
"We talked to the leaders and we will be back for next season."
Antoine Griezmann has decided to stay at Atletico Madrid
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Griezmann's decision will come as a blow to United boss Jose Mourinho as he looks to replace Zlatan Ibrahimovic.
The Swedish striker is out until the New Year with a knee injury and Mourinho wants to sign a new number nine.
Alexandre Lacazette, Andrea Belotti and Romelu Lukaku have all been linked with moves.