But as cheering crowds streamed into the streets of the capital Bujumbura, sporadic gunfire was heard in the city centre, and it was not immediately clear how much support Niyombare had.
The president is at an African summit in Tanzania to discuss the crisis in his country, but the presidential office swiftly rubbished the declaration by Niyombare, who had been fired as Nkurunziza's intelligence chief in February.
"We consider it as a joke, not as a military coup," presidential aide Willy Niyamitwe told Reuters.
Before Niyombare's announcement, protesters demonstrated on Bujumbura's streets. In some neighbourhoods, they battled past police in an effort to reach the central business district. One policeman was seen opening fire on protesters.
A policeman and a protester clash in BujumburaGoran Tomasevic/ReutersA policeman walks past a burning barricade during a protest against President Pierre NkurunzizaGoran Tomasevic/ReutersA man stands in front of a burning barricade during a protest against President Pierre NkurunzizaGoran Tomasevic/ReutersPolicemen clash with protesters near the Parliament building in BujumburaGoran Tomasevic/ReutersProtesters carry a national flag during a protest against President Pierre Nkurunziza's decision to run for a third term, in BujumburaGoran Tomasevic/ReutersPolice officers run from protesters during a demonstration against President Pierre NkurunzizaGoran Tomasevic/ReutersA protester holds up a dead owl to mock the ruling party whose emblem is an eagleGoran Tomasevic/Reuters
Niyombare made his declaration to reporters at a barracks in Bujumbura after more than two weeks of protests against Nkurunziza's attempt to win a third term.
After the announcement, crowds of people streamed out onto the streets of the capital. There was little sign of the police, hated by protesters for breaking up demonstrations by force, and widely considered loyal to Nkurunziza's party.