One of the world's longest-serving rulers and modern history's most singular characters, Castro defied 11 US administrations and hundreds of assassination attempts.
His younger brother, President Raul Castro, announced the news shortly after midnight (1030 IST Saturday) but gave no details of the cause of death.
Fidel Castro crushed opposition at home from the moment he took power in 1959 to lead the communist Caribbean island through the Cold War. He stepped aside only in 2006 after intestinal surgery.
For his opponents, including thousands of Cuban exiles living in the United States, he was a cruel tyrant.
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Castro eventually lived to see the restoration of diplomatic ties with Washington last year.
President Raul Castro, who took power after his elder brother Fidel was hospitalised in 2006, announced the news on national television just after midnight Friday (1030 IST Saturday).
"The commander in chief of the Cuban revolution died at 22:29 hours this evening," Raul Castro said in a solemn voice.
"In compliance with Comrade Fidel's expressed will, his remains will be cremated early in the morning" on Saturday.
From November 26 to December 4, "public activities and shows will cease, the national flag will fly at half-mast on public buildings and military installations," a statement from the state executive said.
Castro's ashes will be buried in the southeastern city of Santiago on December 4 after a four-day procession through the country, it added.
Castro's death drew strong reactions from world leaders.
"The name of this distinguished statesman is rightly considered the symbol of an era in modern world history," said Russian President Vladimir Putin in a telegram to Raul Castro.
"Comrade Castro will live forever," said Chinese President Xi Jinping in a message read on television. "Castro was "a great man of our time... History and people will remember him."
French President Francois Hollande said Castro "represented, for Cubans, pride in rejecting external domination."
Venezuelan President Nicolas Maduro, Cuba's main ally in the region, said on Twitter: "It is up to us to continue his legacy and carry his flag of independence.