She and her former husband Nelson Mandela, who were both jailed, were a symbol of the country’s anti-apartheid struggle for three decades.
However, in later years her reputation became tainted legally and politically.
Crowds of mourners and political figures flocked to her home in Soweto, in Johannesburg, after news of her death broke.
Family spokesman Victor Dlamini confirmed earlier on Monday that Mrs Mandela “succumbed peacefully in the early hours of Monday afternoon surrounded by her family and loved ones” following a long illness, which had seen her go in and out of hospital since the start of the year.
Mrs Madikizela-Mandela was born in 1936 in the Eastern Cape – then known as Transkei.
She was a trained social worker when she met her future husband in the 1950s. They went on to have two daughters together.
They were married for a total of 38 years, although for almost three decades of that time they were separated due to Mr Mandela’s long imprisonment.
It was Mrs Madikizela-Mandela who took his baton after he was jailed for life, becoming an international symbol of resistance to apartheid. She too was jailed for her role in the fight for justice and equality.
To her supporters, she became known affectionately as “Mother of the Nation”.
In a televised address President Cyril Ramaphosa – whom Mrs Madikizela-Mandela praised earlier this year – called her as a “voice of defiance” against white-minority rule.
“In the face of exploitation, she was a champion of justice and equality,” he said on Monday.
“She as an abiding symbol of the desire of our people to be free”.
Retired archbishop and Nobel laureate Desmond Tutu said she was a “defining symbol of the struggle against apartheid”.
“Her courageous defiance was deeply inspirational to me, and to generations of activists,” he added.
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