The Serbian Basketball Federation received permission from the Kings this week to hire Kokoskov, according to Stein.
The 47-year-old is no stranger to international success after leading a Slovenian squad featuring Luka Doncic and Goran Dragic to a EuroBasket title in 2017.
Serbia failed to secure an automatic berth at the 2020 Games following a fifth-place finish at last summer's FIBA World Cup. The country will compete in a last-chance Olympic qualifying tournament in June.
Serbia will be a medal favorite if the team reaches the 2020 Tokyo Games.
The Phoenix Suns fired Kokoskov after the 2018-19 campaign. He posted a 19-63 record during his only season as head coach of the club.