The midfielder has won a new contract to 2021.
"I am very happy to be able to extend my contract here, it is the club of my life and it has been a dream since I was a child," Llorente said to reporters afterwards.
"I am full of patience, I know how young I am and the level that is so high in this club, but I have a desire to learn and grow."
Llorente received a standing ovation upon his return to Alaves, where he had spent last season on loan, and it clearly affected him.
"The ovation was incredible," he continued.
"But now that stage [of his career] is over.
"Now I'm with great players, they give me experience and it is where I can improve, it is where I will grow as a footballer."