The constitution provides for the speaker of Parliament to take over in such a situation. The court ruled, however, that “the interim period is not necessary and that … Ndayishimiye must be sworn in as soon as possible”, the government said in a statement posted on Twitter on Friday.
The statement did not say when the swearing-in would be conducted.
There had been uncertainty as to who was in charge in Bujumbura since the government announced Nkurunziza’s death on Tuesday.
Observers were worried about possible discord over the succession among the ranks of Burundi’s powerful group of generals that might have sparked unrest.
Ndayishimiye was declared the winner of the country’s May 20 vote after fending off a challenge from the opposition’s Agathon Rwasa, and was officially due to be sworn in in August.
Nkurunziza leaves behind a deeply isolated country in political and economic turmoil after his divisive 15-year rule.
His controversial decision in 2015 to seek a third term in office prompted protests and a failed coup, with violence causing at least 1,200 deaths, some 400,000 fleeing the country amid a climate of fear marked by a crackdown on the opposition and media.
The United Nations human rights investigators have said the period since 2015 has been marked by likely crimes against humanity committed by state forces, citing extrajudicial executions, arbitrary arrests, disappearances, torture and sexual violence. The government denied the allegations.
Nkurunziza’s decision not to run in the May 20 election shocked many, as it came after the constitution was changed to allow him to do so.
His successor, Ndayishimiye, 52, was handpicked by the governing party’s core group of powerful generals, and won the election with 68.7 percent votes. Opposition claims of widespread fraud were dismissed by the Constitutional Court.
Nkurunziza, named last year “supreme guide for patriotism”, was expected to continue to have a significant say in the country’s politics.
“In principle, it is an opportunity for him [Ndayishimiye] to free himself, in the sense that we would have expected Nkurunziza to play an important role in the future,” said Richard Moncrieff, an expert with the International Crisis Group (ICG).
However, some observers have said he may run into trouble with the generals if he tries to introduce reforms or improve the human rights situation in the country.