The striker made eight La Liga starts before leaving his boyhood club for Juve in 2014 for a fee that media reports put at 20 million euros (£17.39 million).
He won back-to-back league and cup doubles in Italy but Real exercised their buy-back clause on him in June for around 30 million euros.
Morata was officially presented at the Bernabeu stadium in Madrid on Monday in front of 3,000 supporters.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"I'm at the most difficult club in the world to play and score goals for but I'll give my life for that because I'm a Real Madrid fan," he told reporters.
"It has been a long two-year wait but sometimes you need to mature. I'm here to ... stay for as long as possible."
Morata faces the daunting task of squeezing into a dynamic forward line that contains Cristiano Ronaldo, Gareth Bale and Karim Benzema.
"I said I wanted to be where I was wanted and here I am," he said. "It would have been easy for the club to sell me and I would have got them money but they have shown faith in me."
Despite winning a glut of medals in Italy and scoring vital goals in the club's run to the 2015 Champions League final, including knocking Real out in the semis, Morata was not an automatic starter, making just 27 Serie A starts for Juve.
He scored three goals in four games for Spain at the 2016 European Championship.
(Editing by Nina Chestney)
