Mr Mandela led South Africa's transition from white-minority rule in the 1990s, after 27 years in prison for his political activities.
He had been receiving intensive medical care at home for a lung infection after spending three months in hospital.
Announcing the news on South African national TV, President Jacob Zuma said Mr Mandela was at peace.
"Our nation has lost its greatest son," Mr Zuma said.
"Although we knew that this day would come, nothing can diminish our sense of a profound and enduring loss."
Mr Zuma said Mr Mandela - who is known affectionately by his clan name, Madiba - had died shortly before 21:00 local time (19:00 GMT). He said he would receive a full state funeral, and flags would be flown at half-mast.
Crowds have gathered outside the house where Mr Mandela died, some flying South African flags and wearing the shirts of the governing African National Congress, which Mr Mandela once led.
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http://www.bbc.co.uk/news/world-africa-25249520