Danish international Wass has played much of this season in midfield at Estadio Mestalla, and Simeone has also been impressed by his displays there.
The coach has given the green light to the deal and approves of his versatility and experience in LaLiga Santander, meaning he won't need any time to adjust to the competition.
Atletico's limited budget and wage cap mean that the club were unable to pursue a world-leading right-back in the winter transfer window.
The transfer has now been completed for a fee of 2.7 million euros plus add-ons following weeks of negotiations.
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