The 23-year-old was officially unveiled as an Atleti player on Thursday having signed for the La Liga champions from Real Sociedad for a reported fee of €30million.
Griezmann told reporters Atletico's ambitions mirrored his personal goals and claimed it was easy for the capital club to convince him to leave Sociedad's Anoeta stadium for the Vicente Calderon.
"Atleti showed their interest in me a long time ago. This is a great club with a great project," the attacking midfielder said.
"[UEFA] Champions League finalists and league champions - I didn't think twice about it."
Atletico won their first league title in 18 years last season, while they went within a minute of claiming the Champions League title before losing 4-1 in extra-time to city rivals Real Madrid.
With Diego Simeone's side having also claimed the Copa del Rey in the 2012-13 season, Griezmann said he has joined a team that can help him win silverware.
"I have come to learn; I needed a jump up and knew that this was my big chance," he said.
"I hope to learn a lot from my teammates and the manager. I'm an ambitious player. We will be all out to win all the titles."
Despite having played a part in all five of France's World Cup matches, Griezmann denied he is a certainty to be included in Atleti's starting XI for their first game of the season - the Supercopa de Espana.
Atletico will take on Real in the two-legged Supercopa on August 19 and 22.
"Before anything else, I have to train hard first and show that I am at a good enough level to be in the team," he said.
"There is still time to train before the Supercup; in big games you have to give your best."
Griezmann has yet to link up with the rest of Simeone's squad, as Atletico have spent the past week in the United States and Mexico.
The Frenchman leaves Sociedad after 201 appearances in all competitions for 52 goals.