The World Cup victor signed a five-year contract last June but Saturday's La Liga match against Levante will be his last for the club.
"I spoke with Griezmann and he said to me there was a possibility of him coming. when he made the decision, he said we could record it".
Griezmann hasn't felt it necessary to film another "will he, won't he" special this time around, instead opting for the no-nonsense approach of confirming his decision to leave.
Griezmann was closely linked with a move to Manchester United earlier in the season, but it now seems most likely he will remain in La Liga at Barcelona.
The club posted a goodbye message from the player where he thanks the fans for the five years with the team.
"Thank you very much for everything".
Barcelona will pay the buyout clause in Griezmann's contract of 120m euros, BBC Sport understands.
"I have enjoyed a lot, I have left everything in the field, I have tried to behave well, I have tried to give joy to the people who have come to the Metropolitano and also away from home, and I only have gratitude for all of you". I just put the camera there to see how hard it is.
The Frenchman has scored 133 goals in 256 appearances for Atletico since joining from fellow Spanish outfit Real Sociedad in 2014.
In five seasons with the club, Griezmann has won three trophies, including the 2018 Europa League title.