Atletico Madrid have been looking for a new goalkeeper since Leo Franco and Gregory Coupet both decided to leave the club at the end of the season.
Asenjo, who reportedly rejected offers from Barcelona and Fiorentina to have regular first-team action in a Champions League side, will sign a four-year contract with the Spanish capital club.
The 20-year-old keeper will be presented at the Vicente Calderon on Monday at 1300 CET after completing a medical with the club.
Meanwhile, Atletico have confirmed that striker Diego da Silva Costa will play at Valladolid next season on loan as part of the deal for Asenjo.
