Atletico and Real Sociedad announced on Monday that they had agreed a deal for the 23-year-old, believed to be worth around 30million euros (£24m), and the forward completed the move on Tuesday following a successful medical.
Atletico sporting director Jose Luis Caminero has expressed his delight at finally signing the forward, who originally declared his interest in joining Los Rojiblancos back in 2011.
"I'm very happy that we have secured a deal for his arrival," Caminero told the club's official website.
"Antoine was a priority for us and thankfully we've made it a reality. He is one of the best players in our league, as he demonstrated with Real Sociedad.
"He can play perfectly on the wing or behind the striker due to his speed; he can score goals, he has a great shot on him and he is a magnificent assist provider.
"His signing is great news for our our club."
Although born in France, Griezmann joined Real Sociedad's academy aged 13, making his first team debut in 2010. He was vital to the Basques finishing fourth in the Primera Division in 2012-13 and qualifying for the Champions League, and last term he scored 20 goals as the club earned a place in the Europa League.
The forward bade farewell to the San Sebastian side in a press conference on Monday, declaring: "I spent 10 incredible years here. I came as a boy and leave as a man."
Speaking on Tuesday, former team-mate and close friend Alberto de La Bella said it was "the right time" for Griezmann to move on.
"He has had a great year, he went to the World Cup and La Real have earned a lot of money (from the move) so everyone is happy," said the defender.
"He has taken a step to continue growing and right now we wish him all the best and we're going to keep supporting him."