The Spain striker endured a frustrating last year at Athletic Bilbao after a falling-out with coach Marcelo Bielsa but says he feels "liberated" in Turin
The Spain striker, 28, completed his move to the Serie A champions following a pre-contract agreement with the club in January.
Llorente's nine-year association with Athletic turned sour towards the end after it became public he wanted to leave the club and was consequently dropped by former coach Marcelo Bielsa and lost his place in the national team.
"The move to Juventus was liberating for me," he told Tuttosport.
"The reception of the fans was something spectacular. Ever since I arrived, I've been happy to wear a jersey as prestigious as that of Juventus.
"I'm living the dream - growing as a player and I came to the best team to do so.
"The day of the presentation at the Juventus Stadium was very impressive. The stadium and especially the museum. I've never seen a football museum. It was great."
Llorente has signed a four-year deal with the Bianconeri and says he is already adapting well to life in Italy, having joined the club at the start of July.
"I have already made friends with everyone in the dressing room,” he told reporters. "For me it was very important to learn Italian before getting here.
“I'm glad I made the effort to learn – I already feel like a part of this group."
The forward joins striker Carlos Tevez and defender Angelo Ogbonna as recent recruits of Juventus.