The Spanish champions announced on Monday that they had agreed a deal with Sociedad for Griezmann, who scored 16 goals in 35 La Liga appearances last term.
And, following the successful completion of a medical, the 23-year-old has put pen to paper on a six-year contract at the Vicente Calderon.
Atletico's director of football Jose Luis Caminero told the club's official website: "[We're] very happy to finalise the agreement.
"Antoine was a priority for us and fortunately we have made it a reality.
"He is one of the most important players in our league and showed that at Real Sociedad.
"He operates perfectly both on the wing and as a playmaker. His arrival is great news for our club."
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