The 29-year-old midfielder penned a four-year deal with the Basque side after requesting a transfer from the Vicente Calderon team.
Athletic Bilbao completed the signing of Raul Garcia from Atletico Madrid.
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 euros ($44.