“The deal has been finalised today and he will become a Lazio player in the coming days.
“At this stage though it is not known exactly how much the fee will be.
“We do know, however, that this will be the biggest sale in the club’s history.”
Milinkovic-Savic made 24 appearances and scored five goals for Genk during his one season in the Belgian Pro League after joining from Vojvodina in 2014.
The Serbian won the Bronze Ball at the Under-20 World Cup after his country won the competition in New Zealand.