The midfielder joined Diego Simeone's side for a reported €40million fee after failing to win regular minutes across town.
Llorente, 24, made seven appearances in LaLiga last season, six fewer than in the previous campaign.
Atleti appear set to use him as replacement for the in-demand Rodri and presented Llorente with the Manchester City target's number 14 shirt at a presentation on Friday.
"The coach talked with me and welcomed me, he told me he trusts me," Llorente said of his decision to move.
"I wanted to join an ambitious project, and most importantly at a place where they trusted me and where they supported me.
"I found both things here at Atletico Madrid. I was very attracted to club's project and when the interest arose I did not hesitate to come."
Llorente, a former Spain Under-21 international, joins his father, Paco, and grandfather, Ramon Grosso, among the players to have represented Madrid's two biggest clubs.
"I know it's an uncommon change [of teams] but it was the best for me and I'm really happy to be here," he said.
"I come here with my will to work and my commitment to help the team in whatever it needs. I will fight with them to defend this shirt."