In addition, should the player be transferred before 30 June 2020, Dinamo retain a right to 10 per cent of that fee or €2m – whichever figure is the greater.
The midfielder has signed a five-year contract that runs until 30 June 2023.
“I am very pleased to be at Roma, one of the biggest European clubs,” Coric said.
“I have given everything to reach this level, and I cannot wait for the chance to start showing what I am capable of.”
A technically gifted midfielder, Coric made his senior debut for Dinamo in 2014 – a day after his 17th birthday. He went on to make almost 150 first-team appearances for the club over the next four years, scoring 23 goals and providing 24 assists.