The 17-year-old joins the Catalan giants from Dinamo Zagreb for a €2.2 million fee which could rise significantly depending on appearances.
And the Croatia international, who will join Barca's B team before making the step up to the senior squad, said he is looking forward to start playing for his new club.
"This is a great day and I am very happy," he said at his unveiling on Monday.
"I have always been a Barca fan and I know a lot about the club. I have been watching Barca B this season – they are a young team who play great football.
"I can speak a little Catalan. I’m very happy to have been given the chance to play at the biggest club in the world. Hello to all the Barca fans and Visca el Barca!"