The Principality club parted company with former Spain manager Robert Moreno over the weekend after just seven months at the helm.
Kovac had been without a club since he was dismissed as Bayern Munich manager in November 2019.
The former Eintracht Frankfurt boss joined Bayern Munich in the summer of 2018 and led the Bavarians to the Bundesliga title, one DFB-Pokal trophy and one German Super Cup.
A false start to the 2019/2020 season saw his dismissed as manager of the German champions and replaced by Hansi Flick.
"AS Monaco are pleased to announce the arrival of Niko Kovac as head coach. The Croatian has signed on a three-year contract with an option to extend," Monaco said in a statement.
"Niko is recognised for his work both for the national team and ... in club environments, in the development of young talent, the management of experienced players and the ability to achieve very good results," Monaco vice-president Oleg Petrov said.
"I'm convinced that his experience and personality will help us achieve our goals.
Monaco finished ninth in the French Ligue 1 last season after the campaign was ended early because of the coronavirus pandemic.
