The gifted midfielder, who is seen as one of Europe's biggest talents, will continue his career in Serie A after passing the obligatory medical checks
The Croatian champions announced on Wednesday that the midfielder would leave the club for the Nerazzurri after both sides had reached an agreement over a fee believed to be in the region of €11 million, which could rise to €15m.
Kovacic visited the Policlinico San Matteo di Pavia on Thursday for his medical, and the physical examination did not bring any noteworthy issues to the fore.
"Joining Inter is like a dream come true. I do not know how to explain it. I can only say that it is an incredible feeling and that I will do my utmost for the club," the player told Inter Channel.
"When I was still a boy, Inter were winning lots of trophies. I was training and taking part in campuses and Inter were an important team for me.
"They're one of the biggest clubs in Europe and Italy. I'm happy. I've joined a team like this and I hope to stay here for a long time.
"There are lots of great players here, like [Antonio] Cassano and [Fredy] Guarin for example. I hope to be able to do my bit and help Inter in the championship.
"For now all I can do is thank [the fans] and I hope to meet them soon."
The 18-year-old has inked a contract until the summer of 2017 with Inter.