He is reported to have died of a heart attack. Official confirmation of his death came after his residence in the capital, Abuja, was sealed off by troops.
A special announcement on Nigerian radio said that "the head of state, General Sani Abacha, passed away in the early hours of Monday morning".
A uniformed officer stood before the State House in Abuja to announce the general's death to the public. Martial music filled the state-controlled radio airwaves, officially marking his passing.
Some of Abacha's myriad critics and opponents celebrated on the streets of Lagos, Nigeria's biggest city.
But in his home town of Kano, crowds lined the streets to see the funeral cortege.
He was buried quickly, according to Muslim custom.
Reclusive leader
General Abacha had made few public appearances since greeting Pope John Paul on his visit to Nigeria in March, and recently failed to attend a special function in Lagos.
But a report by Nigerian radio on Sunday said the visiting Palestinian leader, Yasser Arafat, had met General Abacha for two hours of talks.
Accompanied by General Abacha, Mr Arafat also inspected a guard of honour and heard a 21-gun salute before being seen off by the president at Nnamdi Azikiwe International Airport.
Nigeria under Abacha
The general seized power in 1993 after cancelling presidential elections.
He steadily consolidated his grip on power, with purges of the army and restrictions on political activity.
After the execution in 1995 of nine opposition activists, including Ken Saro-Wiwa, and with the presumed winner of the 1993 elections, Chief Moshood Abiola, still in jail, Nigeria was suspended from the Commonwealth and became diplomatically isolated.
Yet it spearheaded the African military intervention that restored Sierra Leone to civilian rule in March 1998.
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