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."
Everton also released a statement, which read: "Everton have completed the signing of talented goalkeeper Joel Robles.
"The 23-year-old glovesman arrives at Goodison Park from Atletico Madrid on a five-year deal for an undisclosed fee."
Robles must now compete with long-time Everton No.1 Tim Howard for the role of first-choice goalkeeper at Goodison Park and it's a challenge that the Spaniard is ready for.
"It is a great honour to come to this club and work with Tim," Robles told Everton's official website.
"He is a great, great goalkeeper and I am looking forward to learning a lot from him.
"Obviously we will be competing together and it's the manager's decision at the end of the day about who he chooses."
He added: "I can't wait to get started at such a big club. Roberto Martinez being here was a major factor in me coming here.
"I firmly believe that he will take Everton to even greater heights. We are all here to achieve that aim. I am a very ambitious goalkeeper, so continuing in the Premier League is superb.
"I think my physical presence is one of my major attributes that I think goes well with the type of football in the Premier League.
"I enjoyed the Premier League last year. It is clearly the most important league in the world. I am just delighted to have the opportunity to continue that at such a great club like Everton."