General Godefroid Niyombare, a powerful former intelligence chief who was sacked earlier in the year, announced via a private radio station that the president had been overthrown hours after he left for neighbouring Tanzania for talks with regional leaders.
He also ordered the closure of Bujumbura airport and the landlocked central African nation's borders.
The outcome of the coup was uncertain, however, with the presidency dismissing what it said was an "imaginary coup" and vowing the perpetrators would be brought to justice. The Tanzanian government said President Nkurunziza was flying back home.
"President Pierre Nkurunziza is removed from office, the government is dissolved," General Niyombare said in the dramatic broadcast on the Insaganiro radio station, which sent opposition supporters into the street in celebration.
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"All people are asked to respect the lives and property of others," said the general, vowing he was committed to the democratic process and would form a "committee for the restoration of national harmony" and work for "the resumption of the electoral process in a peaceful and fair environment."
His announcement prompted hundreds of civilians to run through the streets of the impoverished country's lakeside capital, cheering "victory" and waving the national flag.
Over 20 people have been killed and scores wounded since late April, when Burundi's ruling CNDD-FDD party -- which has been accused of intimidating the opposition and arming its own militia -- nominated Nkurunziza to stand for re-election in June 26 polls.
The clashes between security forces and demonstrators have raised fears of a return to widespread violence in Burundi, which is still recovering from a brutal 13-year civil war that ended in 2006. Hundreds of thousands of people were killed in the conflict.
Asked to rule on the issue, Burundi's constitutional court found in his favour but not before one of the judges fled the country, claiming its members were subject to death threats.
The African Union, European Union and United States have condemned the third-term bid by Nkurunziza, a former rebel leader from the Hutu majority and born-again Christian, who believes he ascended to the presidency with divine backing.