The striker has joined the Europa League holders after becoming surplus to requirements at Juventus
The striker has signed a three-year contract with the Europa League holders, while his release clause has been set at €20 million.
Juventus had been holding out for a fee, but have reached an agreement with Llorente to terminate his contract.
The 30-year-old has spent the last two seasons in Turin, scoring 27 goals in 92 matches, but was surplus to requirements following the summer signings of Paulo Dybala, Mario Mandzukic and Simone Zaza.
The former Athletic Bilbao man will also be keen to replicate his form from his first spell in Spain. He enjoyed nine seasons at San Mames, where he scored 111 goals in 327 games before leaving for Juve.