The 18-year-old will undergo a medical with the Nerazzurri on Thursday before signing his contract to make him the third expected deadline-day arrival at the Giuseppe Meazza
The attacking midfielder, 18, has successfully negotiated personal terms with Nerazzurri representatives and is due in Milan on Thursday to undergo a medical prior to putting pen to paper on a contract.
In a statement on the Croatian champions' official website, Kovacic said: "It's all happened so fast and I'm still in shock, I don't even know what to say.
"Dinamo are my club and my home, so I find it hard to leave, but an offer from a club like Inter, one of the biggest in the world, simply cannot be refused.
"Of course, it's not completed and I'm still waiting for my medical examination, but I believe that this is just a formality."
The likes of Bayern Munich and Juventus sent out scouts to watch Kovacic in action for Dinamo's youth teams before he broke into the side's first team at the tender age of 16.
The Italian giants were initially expected to replace Wesley Sneijder and Philippe Coutinho with Younes Belhanda and Paulinho, but negotiations for the pair broke down and they have subsequently switched their targets.
Earlier on Wednesday, Stuttgart midfielder Zdravko Kuzmanovic and Atalanta winger Ezequiel Schelotto were reported to be on the verge of joining Inter, and Kovacic looks to be the third player arriving.