"Atletico de Madrid and Real Sociedad have reached an agreement for the transfer of Antoine Griezmann," Atletico said on their website on Monday.
"The young French football player will undergo the corresponding medical examination before signing the contract with our club," they added.
Neither Atletico or Sociedad published financial details of the deal but local media said it was worth 30 million euros (£24 million).
Griezmann, 23, played in all five of France's matches at the World Cup finals in Brazil as they were knocked out in the quarter-finals by eventual winners Germany.
He was called up to France's senior squad for the first time in March and has scored three times in nine games for Les Bleus.
His international career was set back by a suspension for disciplinary reasons handed down by the France football federation (FFF) when he was playing for the Under-21 side, reportedly after an unauthorised late-night excursion.
Once the ban was lifted, France coach Didier Deschamps wasted little time in calling him into the side and he was a surprise inclusion in the squad for Brazil ahead of Samir Nasri.
Griezmann had another fine season for Sociedad last term and his 16 goals in 31 La Liga games helped the Basque club finish seventh and qualify for the Europa League.
Born in Macon in central France, he joined Sociedad at the age of 13, and after breaking into the first team helped them win promotion back to the top flight.
He was a key performer in successive French youth sides and helped the Gallic nation win the European Under-19 Championship in 2010 and secure a fourth-place finish at the Under-20 World Cup in Colombia a year later.