Sir Laurens' daughter, Lucia Crichton-Miller, said he had died peacefully at his home in Chelsea on Sunday night. A 90th birthday party, organised by the Prince of Wales, had been cancelled on Friday when Sir Laurens became unwell.
The Prince was said to be "very saddened" at the death of the close friend and adviser. Sir Laurens had been "a dear friend for a very long time".
Greenpeace hailed Sir Laurens as a man who had "inspired" people's interest in the exploration and protection of the natural world. A spokeswoman said: "His writings helped 20th century men and women retain a vision of nature, without which environmental protection will be the poorer."
Born on a bush farm in Orange Free State in 1906, Sir Laurens was the 13th child of 15. Although his first love was the South African wilderness, he spent his last 27 years in a penthouse off the King's Road. His wife is reported to have told people: "Oh, my husband hasn't left Africa, he just lives in London." Sir Laurens himself said he lived here because there was "too much going on" in Africa that would have distracted him from his writing.
He wrote a total of 25 books. Although some are novels, he is best known for the mixed genre of travel, anthropology, and metaphysical speculation.His first book, In a Province, "the first written by a South African against racial prejudice", was published in 1934. His last, The Admiral's Baby, was published in September.
Sir Laurens described Prince Charles as "a man of vision, of many interests and gifts". He also admired, and acted as an adviser to, Baroness Thatcher. In 1981, he was knighted and, a year later, became godfather to Prince William.
Sir Laurens once said he would like to be remembered as "someone who tried to perform some service for what I think is the overall value in life - expressed by St Paul as charity. Without it no human being has any hope whatsoever".
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