The West African country has instead appointed Germany’s Gernot Rohr.
Rohr’s appointment was announced by the Burkina Faso Football Federation (FBF) on Wednesday, exactly a week after it announced Keshi as one of the three men shortlisted for the job.
Ex-Ghana coach, Milovan Rajevac, was the third candidate on the shortlist.
Sixty-one-year-old Rohr replaces Belgian Paul Put who left by mutual agreement after their first-round elimination from the Africa Cup of Nations (AFCON) in Equatorial Guinea last month.
Put led the side to the 2013 CAN final in South Africa where they were narrowly beaten 1-0 by the Keshi tutored Super Eagles of Nigeria.
The duration of Rohr’s contract was not revealed although it was confirmed he will also coach the Burkina Faso Olympic team.
He played for 17 seasons as a defender, including spells with Bayern Munich and Bordeaux, before moving into coaching in 1990.
Rohr led Bordeaux to the 1996 UEFA Cup final, where they were beaten by Bayern, and also coached at Nice, Young Boys, Ajaccio, Nantes and Tunisian side Etoile Sahel before his first national job at the helm of Gabon between 2010 and 2012.
His most recent posting was as coach of Niger between 2012 and 2014.