The Brazilian left-back has joined the Madrid outfit on a four-year deal after Atletico and Granada agreed a reported transfer fee of 10million euros (£8.1m).
Siqueira spent last season on loan at Benfica, where he won a domestic treble and reached the Europa League final, but joins an Atletico side that will have a very different look to it from the team that beat Barcelona and Real Madrid to the title and reached the Champions League final.
David Villa has already left to join MLS side New York City, top scorer Diego Costa looks set to move to Chelsea, and question marks remain over the future of Joao Miranda, Filipe Luis, Thibaut Courtois and Tiago Mendes.
However, Siqueira is confident the team can repeat last season's heroics.
"Here no one talks about one season, people are talking about an entire era of success," he told reporters at his presentation on Wednesday evening.
"Of course we can do it again, that is what we will work towards."
Siqueira's signing has been viewed as preparation for Atletico selling Luis, but the defender refused to be drawn on whether he would share a dressing room with his compatriot, declaring: "I'm here to talk about me."
Of Luis, he said: "We have been friends since we were young.
"This is an important club and I have to be professional. I have come here to contribute, to grow and to learn."
The defender also spoke of his delight at working under Diego Simeone.
"Working with a coach like him is going to be amazing," he said.
"Atletico are a joy to watch, because the project is everything you see: results. Any footballer would want to be a part of this club.
"This is an unforgettable day, as I can say that I play for the champions of the Spanish league."