The 21-year-old joined the Bianconeri from Real Madrid in July, after failing to earn a regular spot at the European champions.
"The adventure in Italy is going very well, and I could not feel better," Morata told Marca. "I love the city and my teammates. I have been well received and feel great physically. It's the best place that I could have ended up.
"Playing for Real Madrid was a dream, but now I'm at Juventus and ready for a new challenge. Playing for Juve is another dream of mine. I will go step by step to achieve all of my goals.
"Leaving Real Madrid was difficult, but if a team like Juve comes your way and place their trust in you... Let's just say that I could not ask for anything better. The main thing is that I wanted to feel important, so I like how the Coach talks to me a lot. I feel part of the team and useful to the squad."
Morata scored nine times for Real Madrid last season.