Prof Hawking passed away peacefully at his home in Cambridge in the early hours of this morning.
Tributes have already begin pouring in to the great man, known for his work on black holes and relativity, and popular science books including A Brief History of Time.
In a statement his children, Lucy, Robert and Tim, said: "We are deeply saddened that our beloved father passed away today.
"He was a great scientist and an extraordinary man whose work and legacy will live on for many years."
Prof Stephen Toope, vice-chancellor of Cambridge University, paid tribute, saying: "Professor Hawking was a unique individual who will be remembered with warmth and affection not only in Cambridge but all over the world.
"His exceptional contributions to scientific knowledge and the popularisation of science and mathematics have left an indelible legacy. His character was an inspiration to millions. He will be much missed.”
A man of great humour, he became a popular ambassador for science and was always careful to ensure that the general public had ready access to his work.
His book A Brief History of Time became an unlikely best-seller although it is unclear how many people actually managed to get to the end of it.
He appeared in a number of popular TV shows and lent his synthesised voice to various recordings.
Stephen William Hawking was born in Oxford on 8 January 1942. His father, a research biologist, had moved with his mother from London to escape German bombing.
Hawking grew up in London and St Albans and, after gaining a first-class degree in physics from Oxford, went on to Cambridge for postgraduate research in cosmology.
As a teenager he had enjoyed horse-riding and rowing but while at Cambridge he was diagnosed with a form of motor neurone disease which was to leave him almost completely paralysed.
As he was preparing to marry his first wife, Jane, in 1964 his doctors gave him no more than two or three years of life.
But the disease progressed more slowly than expected. The couple had three children, and in 1988 - although Hawking was by now only able to speak with a voice synthesiser following a tracheotomy - he had completed A Brief History of Time - a layman's guide to cosmology.
It sold more than 10 million copies, although its author was aware that it was dubbed "the most popular book never read".
He received honorary degrees, medals, prizes and awards throughout his career and was honoured with a CBE in 1982. He was reportedly offered a knighthood in the 1990s but later revealed he had turned it down over issues with the government's funding for science.
Hawking discovered the phenomenon which became known as Hawking radiation, where black holes leak energy and fade to nothing. He was renowned for his extraordinary capacity to visualise scientific solutions without calculation or experiment.
But it was perhaps his "theory of everything", suggesting that the universe evolves according to well-defined laws, that attracted most attention.
"This complete set of laws can give us the answers to questions like how did the universe begin," he said. "Where is it going and will it have an end? If so, how will it end? If we find the answers to these questions, we really shall know the mind of God."
Hawking's celebrity status was acknowledged even by The Simpsons - he was depicted drinking at a bar with Homer, suggesting he might steal Homer's idea that the universe is shaped like a doughnut.
He appeared in a special documentary about BBC comedy series Red Dwarf during which he spoke about why he enjoyed the show and also starred in Star Trek: The Next Generation as a hologram of his image.
The rock group Pink Floyd used his distinctive synthesised voice for the introduction to Keep Talking, on their 1994 album The Division Bell.
Undeterred by his condition, he continued his work as Lucasian Professor of Mathematics at Cambridge University, and in 2001, his second book - Universe in a Nutshell - was published.
In 2014, the film The Theory of Everything was released, based on Jane Hawking's account of their courtship and marriage. Hawking himself met Eddie Redmayne as part of the actor's preparation for taking on the role of the scientist.
In a series for the Discovery Channel, he said it was perfectly rational to assume there was intelligent life elsewhere but warned that aliens might just raid earth of its resources and then move on.
Hawking also predicted the end of humanity from global warming, a large comet or a new virus.
He collaborated with Russian investor Yuri Milner in 2015 to work on projects to find evidence of alien life.
He once wrote that he had motor neurone disease for practically all his adult life but said that it had not stopped him having an attractive family and being successful in his work.
"It shows," he said, "that one need not lose hope."