The 23-year-old was part of France's squad at the 2014 Fifa World Cup and helped the side to reach the quarter-finals in Brazil.
Griezmann, who had been with the Basque club for 10 years, has signed a six-year contract with the Spanish champions.
He joins Mario Mandzukic in signing for Atletico this summer.
Atletico Madrid have signed winger Antoine Griezmann from Real Sociedad for an undisclosed fee, reported to be £24m.