The 25-year-old keeper spent last term on loan at Villarreal and made 35 La Liga appearances for the club.
His season-long loan deal included an option for Villarreal to make the deal permanent, a right they exercised following his impressive performances.
The former Spain Under-21 man is pleased to have made the switch official and has tipped the club to improve on their sixth-placed finish last term.
"I've always said since I arrived - Villarreal was my only option," Asenjo told the club's official website.
"I can not be happier. The club has made an effort (to sign me) - I thank you heartily, and now I have to return that trust you have placed in me.
"From day one I have felt the love of my peers, everyone in the club, the fans of El Madrigal and (it) felt like home since I put (my) first foot in this club.
"I am very excited about this new season which adds another challenge – to qualify and play the next edition of the Champions League.
"I think the team is ready to do well and we all have the same challenge in mind, but (we) will have to work hard for it."
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