Goal.com understands that the Belgian national has beaten off stiff competition from a host of candidates including Uganda's Bobby Williamson to the post.
Amrouche is set to replace Frenchman Henri Michel who quit in a huff in last December following what he termed as a 'contractual dispute'.
After his unveiling, Amrouche's first assignment will be to prepare the national team for a must win 2014 World Cup qualifier away to Nigeria in March.
"He will be coming in early this week to finalize on the deal before his unveiling. The federation believes he is the right person to steer the team mainly because of his experience and exposure of East African football."
Amrouche, who featured for USM Algier during his playing career, will bring a wealth of experience to the Stars, having handled Burundi national team and Congolese club DC Motema Pemba during his one and a half year experience in the dugout.
Th Belgian will become the fourth manager to handle Kenya in the last 15 months. He will be assisted by James Nandwa. Amrouche began his managerial career in 1988 by coaching the youth ranks of local club OMR El Annasser while playing for the senior team.
He held the same role during his playing stints with USM Alger and RC Kouba. In 2002, he was appointed as the manager of Congolese club Daring Club Motema Pembe.
In 2007, Amrouche became the coach of Burundi. On January 1, 2011, Amrouche turned down an offer to take over the vacant managerial role of Algerian club ES Sétif, preferring to continue in his role with the Burundi team.
He resigned as the coach of Burundi, just a day after a 2-1 win against Zimbabwe in the 2013 Africa Cup of Nations qualifiers.