The 63-year-old Belgian was officially unveiled by the Cameroon Football Federation (Fecafoot) on Thursday as he signed a two-year contract.
Broos has not managed at national team level before but insisted he is "not afraid" and demands to be respected.
"I will never accept intrusion in my job as a coach. I am the coach and I take the decisions," he said.
"It is the first time I will be training a national team and there is always a beginning but I hope for good results and I am not afraid to take the post.
"I have always been passionate about African football and Cameroon has a rich football history having participated at World Cups and won the Africa Cup of Nations.
"They have good players and this, coupled with the prospect of qualifying for and playing in two big competitions, was a big attraction."
Fecafoot has set Broos two main objectives: to qualify the team for the 2017 Nations Cup and also for the 2018 World Cup.
His first task is to prepare for the Cameroon's 2017 Nations  qualifier against South Africa on 26 March.
Broos admitted he will initially rely on Alexandre Belinga, who was the interim coach, for information and to get up to speed.
And he will need to make a fast start to the job in order to win over some skeptical Cameroon fans who are unsure if he is the right man to lead the Indomitable Lions.
Meanwhile, former Cameroon captain Rigobert Song has been appointed coach of Cameroon's national team for locally-based players.
He replaces Martin Ndtoungou Mpile, who took the team to the quarter-finals of the African Nations Championship in February.
New Cameroon coach Hugo Broos has made it clear he will not tolerate any interference in his work.