The 18-year-old playmaker, who has already drawn comparisons to Luka Modric, will command a fee of around 11million euros, according to several reports.
"It all happened so fast and I'm still in shock, I do not even know what to say," Kovacic told Dinamo's website of the deal.
"Dinamo is my club and my home, so I find it hard to leave, but an offer from a club like Inter Milan, one of the biggest in the world, cannot be refused.
"Of course, it's not over and I'm waiting for my medical examination, but I believe this is just a formality."
Kovacic joined Dinamo as a youngster in 2007 from Linz. He was born in the Austrian city but is eligible for Croatia through his parents.