"Niko is recognised for his capacity to obtain very good results and the progression of young talents," Monaco vice-president Oleg Petrov said.
Sources told ESPN that Monaco players were unaware Moreno was going to be sacked when they trained with the former Spain head coach early on Saturday after beating Cercle Brugge 2-0 in a friendly on Friday.
Leonardo Jardim, Franck Passi, Thierry Henry, Jardim again and Moreno have all managed the club in the last 18 months.
After winning the league in 2017, Monaco have experienced a downturn of form, finishing 17th and ninth in the last two seasons.
Paul Mitchell was appointed sporting director of the club in June with the mission of reducing the squad size and building a team capable of competing in the Champions League.
Mitchell said: "Niko represents the highest level of experience both as a former player and head coach. He has constantly shown an ability to win with Bayern Munich, one of the biggest clubs in the world and winning while in a re-building process at Frankfurt.
"Niko was a key influence in turning Frankfurt into a top performing team in Germany, guiding the team twice in consecutive years to the cup final and leaving them with a place in European competition."
Kovac's first training session with the club is scheduled for Monday.