The Spanish side have won the race to sign the France international after meeting his £23.7m release clause, with the 23-year-old now set for a medical with the league champions
Goal exclusively revealed the Liga winners' interest earlier this month, with Atleti fighting off interest from Monaco to seal the Frenchman's signature in a £23.7 million deal.
"Atletico Madrid and Real Sociedad have reached an agreement for the transfer of Antoine Griezmann," read a statement on the official Atletico website. "The young French player will undergo a medical before signing a contract with our club."
The 23-year-old came through the ranks of the Sociedad youth academy and has become a key player for the Basque side since his breakthrough to the first team in 2009-10.
Griezmann, who was part of the France squad that made it to the quarter-finals at the World Cup in Brazil, has made over 200 official appearances for Real Sociedad and bagged 16 Liga goals last season.
"He’s a brilliant player," Atletico coach Diego Simeone told reporters ahead of the club's friendly match against San Jose Earthquakes. "He is very quick and can give us a lot of options in attack."
The gifted attacker had also caught the attention of Arsenal and Tottenham, as well as Ligue 1 runners-up Monaco, but will continue his career at the Vicente Calderon instead.
He will become Atletico's fourth summer signing after the previous arrivals of Miguel Moya, Jan Oblak and Mario Mandzukic.