Griezmann announced his intention to stay at Atletico in a televised documentary prior to France's first game at the World Cup.
The forward then confirmed his plans to remain with the La Liga side for the 2018-19 season by extending his contract at the Wanda Metropolitano by a further year, through to 2023.
Barcelona have reportedly tried to sign Griezmann two years in a row but the Catalan giants have been unable to lure him away from Atletico.
However, that speculation may have contributed to moments of discord between Griezmann and the fans, with Atletico boss Diego Simeone warning in February the supporters risked driving the forward away.
But Greizmann has now said his close connection with the club and their supporters is the reason he has decided to stay.
"We are family and that is evident in the pitch, we all fight for the same goal," Griezmann told Atletico's official website.
"I always felt loved by everybody, and that's very important for me. We are a very closely-knit team.
"I understand that some fans could get nervous due to uncertainty. It's logical. But I can only have words of thanks for our fans, they are always supporting me and I try to give those signs of affection them back giving my best in the pitch.
"There's nothing that excites me more than hearing them singing my song in the Wanda Metropolitano, it's incredible."
Great news from Russia. @AntoGriezmann has signed his renvovation until 2023, @LucasHernandez until 2024 and Lemar has signed his contract #AúpaAtleti https://t.co/bTPkTFdhIb pic.twitter.com/s0EFsVbX9O— Atlético de Madrid (@atletienglish) June 18, 2018
Griezmann, top goalscorer at Euro 2016, is now turning his attention to ensuring Europa League champions Atleti have a bright future.
"I'm very happy and convinced we'll accomplish great things together," Greizmann added. "This past season, I won my first European title with the club, which was something I had been really trying to achieve. Now, my only wish is to keep on competing in pursuit of more success.
"Since I arrived at the club we have grown so much. We have a brand new stadium which has been praised by everybody and which allows us to empower the growth of the last years. I love the project we are creating, with great players. I thank the big effort the club are doing.
"Miguel Angel Gil [Atletico Madrid CEO] told me his ideas for the next seasons and I got really excited. The project is incredible.”