Brozovic represented his country at last year's World Cup and had been linked with a number of Europe's leading clubs, including Arsenal.
Dinamo previously revealed that they had turned down an offer from Inter for the midfielder, but he will now continue his career at San Siro after the clubs agreed on an initial two-year loan deal with an option to buy.
"I'm happy and sad at once," Brozovic is quoted as saying by Dinamo's official website ahead of his departure.
"Dinamo is my club and I leave here many friends who I will miss, but on the other hand I am happy because I go to a great team and a strong league where I'm waiting for new challenges.
"Of course, Dinamo will always be my club, but I look forward to going to Italy."
Brozovic, capped seven times by Croatia, follows Lukas Podolski and Xherdan Shaqiri in signing for Roberto Mancini's Inter during the January transfer window.
The 22-year-old spent two-and-a-half seasons with Dinamo, winning two league titles and featuring in the UEFA Champions League and Europa League during that time.
