His personal assistant told The New York Times that he died yesterday at his home in New York City from cancer.
Dr Sacks announced in February that his “luck had ran out” after he was diagnosed with the disease.
In an op-ed for the American newspaper, he said that he had multiple metastases in the liver, and was now “face to face with dying”.
“It is up to me now to choose how to live out the months that remain to me. I have to live in the richest, deepest, most productive way I can,” he said.
The London-born academic was the author of several books about unusual medical conditions including Awakenings, The Man Who Mistook His Wife For A Hat and The Island Of The Colorblind.
Awakenings was based on his work with patients who were treated with a drug that woke them up after years in a catatonic state.
The film version, starring Robert De Niro and Robin Williams, was nominated for three Oscars – including Best Picture, in 1991.
Dr Sacks was awarded several honorary degrees recognising his contribution to science and literature, and was made a CBE in 2008 in the Queen’s Birthday Honours.
Tributes to the author were paid on Twitter.
JK Rowling described Dr Sacks as a “great, humane and inspirational” man, adding that he had “a life well-lived”.
The great, humane and inspirational Oliver Sacks has died. He wrote this recently. That's a life well-lived. pic.twitter.com/ZnaKrOzkBm— J.K. Rowling (@jk_rowling) August 30, 2015
The biologist and atheist Richard Dawkins wrote that he “greatly admired him” and was “sad to hear of his death”.
I met Oliver Sacks only twice, but greatly admired him. Sad to hear of his death.— Richard Dawkins (@RichardDawkins) August 30, 2015