The midfielder leaves city rivals Real Madrid for Atletico in a €40m deal.
Llorente said, "It is something unusual, but it was the best for me and I am delighted. I come with all my work and commitment to help the whole team.
"We must aspire to compete and fight for all the titles and I think we have the capacity to achieve it. We have the quality for it."
"I wanted to come to an ambitious project that would trust and bet on me. At Atlético I have both."