Llorente will join Bilbao on a free transfer in June.
"It is not easy for me at the moment," the 27-year-old told AS. "Many people here are with me and love me - but another part of me just wants to leave as quickly as possible.
"I had offers from many teams. But I really liked the Juve project. They have invested heavily in me from the start and have always been clear of their intentions.
"I've always enjoyed the competitive spirit of Italian teams, and for me, Juve are the biggest. The club are also trying to win the Champions League, which, for me, is the title that is the most exciting.
"They are a winning team, with the ambition to keep on winning. It excites me a lot."