The Spanish champions have struck a deal with Granada for the left-back, who agreed a four-year contract at the Estadio Vicente Calderon and has now been unveiled in the capital after passing his medical.
The 28-year-old, who spent last season on loan at Europa League finalists Benfica, did not hesitate to accept Atletico's offer and hopes that the success which they achieved this season can be sustained for a long period of time.
"Today is an unforgettable day. I'm happy and excited," he told reporters at his unveiling. "It is an important day because I can already say that I am at the league champions.
"Of course [we want more success]. That's what we're working towards. We don't speak about a season here but a cycle.
"This Atletico team is impressive," he added. "Watching the team is a pleasure. One of the strengths of this group is physical fitness. Atleti are stronger at the latter stages of the league campaign than others.
"Any player would want to be part of this group - it did not take a second to decide once I knew they were interested.
"The boss has been doing an amazing job. Watching Atletico play is a joy. The project here is about results. Any footballer would want to be a part of this club.
"I haven't spoken to him yet - let him enjoy his holidays - but there's not much to say, you can see what Atleti are about. I really like the idea of playing each game as if it were your last. I hope to settle in as quickly as possible."