Gervais Ndirakobuca - whose nickname 'Ndakugarika' means 'I will kill you' - had been unanimously approved, according to a statement by Burundian parliament released on Twitter.
Ndirakobuca was picked to be PM by President Evariste Ndayishimiye, who last week had warned that unnamed people were plotting to overthrow his government.
In an audio recording Ndayishimiye accused certain people of sabotaging the government by failing to solve a scarcity of key commodities that has fueled resentment among some Burundians.
A senior government official who spoke anonymously said the voice in the audio was that of the president. A call to the president's spokesperson went unanswered.
The central African country has been grappling with shortages of fuel, sugar and other staples for months.
Burundi is one of the world's poorest countries. Over the years, Burundi’s politics have been marred by widespread human rights violations. That includes killings, disappearances, torture and gang rape of government opponents, according to the United Nations.
Prime Minister Ndirakobuca, who replaced Alain Guillaume Bunyoni, is under EU sanctions for his role in quashing demonstrations during political unrest in 2015.