The goalkeeper will join the club on a four-year deal...
The goalkeeper has been widely tipped to leave Valladolid this summer, with Villarreal, Barcelona and Atleti all vying for his services.
It is the capital club who have won the race to secure his signature according to Marca though and he will join on a four-year deal.
The 19-year-old is one of the most highly-rated young goalkeepers in Europe at the moment and his signing will be made official when Atleti return from a friendly next week.
Asenjo looks likely to be the second signing made by Atletico this summer, with a deal for Real Betis defender Juanito already reported to be in place.
Whilst two come in though, it looks like three will go out, with Leo Franco, Gregory Coupet and Angel Bernabe all ready to pursue their goalkeeping careers elsewhere.
Franco is reported to be close to a move to Galatasaray, whilst Coupet could move back to France, and Bernabe has had offers but does not yet have a clear future.
It is thought that Atletico have been after Asenjo for a while, and reports claim that Atletico director Gil Marin, recently met with the Valladolid president to discuss the deal.
It appears that they all but finalised the agreement at the meeting and all that is left to do is decide how much the deal will be worth.
The reported fee is €4 million, with two players also moving from Atletico to Valladolid as part of the transfer.
The players to choose from are thought to be Juan Valera, Cleber Santana, Miguel de las Cuevas and Diego Costa, none of whom are likely to stay with the club beyond the summer.
James Walker-Roberts, Goal.com