Atletico have paid €40m for Llorente.
The midfielder, 24, has signed a five-year deal at the Wanda Metropolitano, where he'll be presented next week.
"I'm very excited," Llorente said ahead of his medical.
"I'm very happy because I wanted to come here. It's a project with ambition and they're betting on me."
Llorente becomes the 11th player to move from the Santiago Bernabeu to Atleti, but he's not worried about integrating.
"I'm not afraid," he explained.
"I come here with calmness, knowing that I gave everything at Real Madrid. I worked as much as I could.
"Now I'm here to work and to give everything for this shirt. I'll do the best I can, and with my work and commitment I want to earn the affection of the fans."