The forward, who is coming off a World Cup-winning campaign with France, was La Blaugrana's chief target ahead of the tournament. But he publicly stated that he would remain with Los Rojiblancos before heading to Russia with Les Bleus in a video labelled "La Decision".
Griezmann was also a target for Premier League side Manchester United the previous summer but signed a new deal with the club after it was confirmed that they would not be able to register any new players due to a transfer ban at the time.
Speaking to French magazine L'Equipe during the current international break, the striker admitted that it was hard to say no to a club of Barcelona's stature but he stayed with Atletico as he felt loved there.
"When you're shown love at home, you don't go elsewhere," he explained. "They did everything possible to make me feel good, including bringing in important players and building a great team."
"It's difficult to say no to teams like Barça but I feel like the base, or the most important piece of the puzzle, that is what made me stay."
Griezmann has scored one goal and assisted another in his three league appearances for Atletico so far this season after scoring 19 times and dishing out nine assists the previous term.
Meanwhile, Barcelona forward Luis Suarez has said he was surprised by Griezmann's decision, also stating that the Frenchman has earned the respect of the football world after resisting what would have been the biggest move of his career.
"[I was surprised]," the Uruguayan admitted during an interview. "But everyone has the right to decide and he's earned the respect of the whole football world."