Morata departed Real for Juve in July on a five-year deal, although the Spanish club have the option to buy the striker back in future.
Spain Under-21 international Morata made his debut for the defending Serie A champions in a 2-0 win over Udinese last Saturday.
Morata's decision to move away from Spain so early in his playing career could perhaps be considered to be a surprising one, especially following a season in which he helped Real win the UEFA Champions League and the Copa del Rey.
However, Morata insists he already feels at home in Turin and is hoping to become a regular under new coach Massimiliano Allegri.
"At Juve I feel very important," Morata told Marca. "Turin is the best place I could be. I get the confidence I needed.
"Now my only hope is to be as happy as possible in Turin. The goal this year is to be a real option for the coach."