The 63-year-old's appointment was announced by the Cameroon football federation (Fecafoot) on their website.
Former international defender Broos made his name as a coach in his home country, leading Club Brugge to two Belgian titles in 1992 and 1996, before also winning the first division while in charge of Anderlecht in 2004.
His most recent job was a five-month stay at Algerian outfit NA Hussein Dey.
Alexandre Belinga had been the interim coach for the Indomitable Lions since German Volker Finke's departure, but will now be one of two assistants to Broos, the other being 36-year-old Belgian Sven VandenBroeck.