The British scientist was famed for his work with black holes and relativity, and wrote several popular science books including A Brief History of Time.
He died peacefully at his home in Cambridge in the early hours of Wednesday, his family said.
At the age of 22 Prof Hawking was given only a few years to live after being diagnosed with a rare form of motor neurone disease.
The illness left him in a wheelchair and largely unable to speak except through a voice synthesiser.
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.”
They praised his “courage and persistence” and said his “brilliance and humour” inspired people across the world.
“He once said, ‘It would not be much of a universe if it wasn’t home to the people you love.’ We will miss him forever.”
A book of condolence is due to be opened at Gonville and Caius College in Cambridge, where Prof Hawking was a fellow.
Prof Hawking was the first to set out a theory of cosmology as a union of relativity and quantum mechanics.
He also discovered that black holes leak energy and fade to nothing – a phenomenon that would later become known as Hawking radiation.
Factfile: Stephen Hawking
- Born 8 January 1942 in Oxford, England
- Earned place at Oxford University to read natural science in 1959, before studying for his PhD at Cambridge
- By 1963, was diagnosed with motor neurone disease and given two years to live
- Outlined his theory that black holes emit “Hawking radiation” in 1974
- In 1979, he became the Lucasian Professor of Mathematics at the Cambridge – a post once held by Sir Isaac Newton
- Published his book A Brief History of Time in 1988, which has sold more than 10 million copies
- In the late 1990s, he was reportedly offered a knighthood, but 10 years later revealed he had turned it down over issues with the government’s funding for science
- His life story was the subject of the 2014 film The Theory of Everything, starring Eddie Redmayne
Note: Content may be edited for length and manner.