Current President Pierre Nkurunziza will not seek re-election.
Ndayishimiye, who hails from the central Burundi province of Gitega, promised to carry on with the current government's programmes if elected.
"This is not a new start," he told a party congress in the town of Gitega after Nkurunziza announced he would be the candidate.
"Much has been done ... we want that by 2027 every Burundian citizen sees change at his home, in his neighbourhood, in his district or where he works."
CNDD-FDD grandees said they settled on Ndayishimiye after he met the required conditions, including understanding Burundi's violent history, respect for former combatants and a vision for developing the country.
He will face off with the opposition Frodebu and CNL parties in the May 20 election. Nkurunziza promised to campaign for him "with all our force and intelligence".
This is the first time that an outgoing Burundian president has picked his successor peacefully, Ndayishimiye said.
The East African nation of 11 million people has suffered colonial occupation, civil war and decades of intermittent massacres.
Nkurunziza and Ndayishimiye are close allies who started out in the CNDD-FDD (Council for the Defence of Democracy-Force for the Defence of Democracy) as rebels in the 1990s.
Nkurunziza became president in 2005 after a peace deal was signed in Tanzania.
His decision to run for a third, five-year term in 2015 sparked widespread protests and violence. His party has welcomed his decision to stand down, conferring on him the title of "Supreme Guide of Patriotism" and lavish perks including a villa worth $530,000.
Burundi is one of the world's poorest countries and lost donor funding after the violence following the 2015 election.
In September, the United Nations warned that police, security forces and the ruling party's youth league, the Imbonerakure, were committing serious human rights violations.
Those included killings, disappearances, torture and gang rape of alleged political opponents. Burundi condemned the accusations.
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