The 24-year-old made 35 appearances during a loan spell at El Madrigal last season, with Atletico using Belgian international stopper Thibaut Courtois as first choice.
Courtois will return to parent club Chelsea for next campaign, but Madrid are still happy for Asenjo, who only made 19 appearances for them after arriving from Real Valladolid in 2009, to leave to join the Yellow Submarine on a permanent basis.
Asenjo told the Villarreal website: "I've said almost since I arrived here that Villarreal were my only choice. I couldn't be happier. I can only feel pleased because everything has turned out well and I can start a new chapter of my career here.
"The club have made an effort to keep me here, which I'm very grateful for, and now I have to return this confidence which they've placed in me."
Atletico are believed to be keen on signing Levante's Keylor Navas as their new number one.