Morata has penned a five-year deal in Turin, while Real will have the right to re-sign the striker until the end of the 2016-17 season.
The Spain Under-21 international has struggled to constantly nail down a first-team place at the Santiago Bernabeu, although he contributed nine goals in all competitions last term.
Ultimately, a stellar forward line of Gareth Bale, Cristiano Ronaldo and Karim Benzema made it difficult for Morata to start games regularly.
However, he will fancy his chances of competing for a spot in Massimiliano Allegri's attacking ranks, alongside the likes of Carlos Tevez and Fernando Llorente.
Morata arrives at the Juventus Stadium for what is the start of a new era for the Italian champions - who parted company with former coach Antonio Conte on Tuesday.
Allegri, appointed as his replacement a day later, will be tasked with building on the three consecutive Scudetti won in Conte's era with Morata his first signing.
Despite struggling for appearances at Real, he picked up a host of honours including the Liga title and two Copa del Rey medals.
His final game for the club saw him feature in the UEFA Champions League final as Real clinched La Decima with a 4-1 win over city rivals Atletico.
