Atletico forward Griezmann has always been targeted by the Nou Camp outfit but the Frenchman rejected them last summer after releasing a video on his decision to stay in Madrid.
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.
"The truth is it has been hard to arrive to this point but I feel it's what I need to do, I want to thank you for all the support you have given me in these five years, where I won my first trophies".More news: The Moon is shrinking: NASA study
Barca look certain to be his next destination with Griezmann, 28, reportedly set on making a move he spurned previous year.
And according to Italian journalist Fabrizio Romano, Barca are already in negotiations with the World Cup victor over a summer move to the Nou Camp.
"Talks ongoing with the player about the contract to finalise the deal (5 years)".More news: Man Utd hero Evra slams Alexis: You only joined for money!
"It has been five incredible years, thank you very much for everything, I will carry you in my heart", Griezmann said in the video that was published via Atletico's Twitter account, which was further confirmation of MARCA's initial report.
"I have chose to leave, see other things, have other challenges and with great difficulty, this is what I feel and I need".
The announcement of Griezmann's Atletico departure comes a little over two months after his fellow countryman and Barcelona defender Samuel Umtiti claimed he regretted not joining the Spanish champions. "He is at a team that plays for him".More news: Myanmar plane lands without front wheel
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