Mr Woods had drawn world attention to the case of Steve Biko, the black consciousness leader who was killed by South African security forces while in detention.
Mr Woods died in hospital near London surrounded by his wife Wendy and five children, his daughter Jane said.
She said the former South African President, Nelson Mandela, had telephoned his good wishes several days ago.
The South African High Commissioner in London, Cheryl Carolus, described Mr Woods as a "truly great son of South Africa".
She said that, though his great life of courage had ended, his spirit lived on with his people.
Active in exile
As editor of the Daily Dispatch from 1965 he forcefully condemned the apartheid government's policy of racial discrimination.
Mr Woods was forced to flee South Africa in 1977 after he was arrested and banned because of his friendship with Mr Biko.
Under a five-year banning order, he was barred from his office and forbidden to travel, write or speak publicly.
He fled South Africa disguised as a priest, and settled in London with his family.
In exile he wrote several books and continued to campaign against apartheid.
He and Mr Biko were made famous by the film Cry Freedom, which was based on his autobiography.
Honoured
Last year, Queen Elizabeth II made Mr Woods a Commander of the British Empire, for his human rights activities.
He first returned to South Africa after 13 years in exile in August 1990.
His last visit was in May, where he attended the wedding of Mr Biko's son, Nkosinathi Biko.