Ndayishimiye is an ally of current President Pierre Nkurunziza who will not seek a new mandate after his controversial election to a third term in 2015 plunged the country into crisis.
"Gen Evariste Ndayishimiye chosen to represent the CNDD-FDD at the 2020 presidential election," the party tweeted during an extraordinary congress at which Nkurunziza was present.
Nkurunziza's tenure has been marked by allegations of grave rights abuses and a crackdown on political freedoms.
Constitutional changes would have allowed him to stay in office until 2034, but he said in 2018 that he would not stand for re-election again.
Ahead of Sunday's congress, Nkurunziza had announced "the beginning of a new page in the history of Burundi and the CNDD-FDD party".
The violent aftermath of the last presidential election in 2015 made Burundi a focus of an investigation by the International Criminal Court for alleged murders, rapes, tortures and disappearances.
Civil unrest left 1,200 people dead and drove 400,000 from their homes.
Ndayishimiye, 52, is already a key member of Burundi's ruling elite.
He has served as interior and security minister and chief of the president's military and civilian cabinet.
Like the current president, Ndayishimiye emerged from rebellion movement against the ruling Tutsi community by ethnic Hutus who gained power after the country's civil war, and was a key signatory of the 2003 ceasefire that ended the conflict.
"He's an approachable, easygoing man, who likes to joke and laugh with his friends," a friend who declined to be identified said of Ndayishimiye.
"But unlike Nkurunziza who is a composed, cold-blooded animal, Evariste Ndayishimiye is rather quick to anger and can lose his temper, with a risk of escalation," the friend said.
A diplomatic source told AFP that Ndayishimiye had a reputation for "openness and honesty, unlike the other generals" having emerge from the civil war.
"He's the best choice, but he will have a hard time prompting change and openness towards the opposition in a party that's dominated by an extremist and sectarian current," the diplomat said.
According to a newly-adopted law, Nkurunziza meanwhile is to stay in a newly-built luxury villa after he steps down, receive a one-off payment of close to $550,000 and a salary for the rest of his life.
It is unclear whether he will stay out of politics, but experts say he is likely to remain influential.
str-fal/jh/har