Robles, who spent last season on loan at the DW Stadium from Atletico Madrid, has signed a five-year deal and follows Antolin Alcaraz and Arouna Kone to the club as new manager Roberto Martinez continues to recruit his former players in the north-west.
Kone arrived on a three-year deal for an undisclosed fee on Monday while Alcarez was signed on a free transfer on Tuesday.
A statement on Atletico's website read: "Atletico Madrid and Everton have reached an agreement for the transfer of Joel Robles to the English club.
"The goalkeeper, who ended last season playing on loan at Wigan, will compete in the Premier League following the agreement reached between the three parties. In our club we wish him luck in this new stage of his career."