The midfielder brings an end to an eight-year spell with the Vicente Calderon side, having completed a medical and being unveiled as the Basque club's newest signing.
Atleti admitted that the move was "at the request" of Garcia, and the former Osasuna man has signed a four-year contract with Ernesto Valverde's team with a release clause of €40 million.
The 29-year-old won La Liga, the Copa del Rey, Europa League, Supercopa de Espana and two Uefa Super Cups at Atleti and reached the Champions League final with Diego Simeone's men in 2014.
Bienvenido al Athletic Club, Raúl García. pic.twitter.com/EsdPxqGTNp— Athletic Club (@AthleticClub) August 31, 2015