He died peacefully in his home in Cambridge in the early hours of Wednesday, his family said.
He was known for his work with black holes and relativity, and wrote several popular science books including A Brief History of Time.
“We are deeply saddened that our beloved father passed away today,” his children said.
At the age of 22 Stephen Hawking was given only a few years to live after being diagnosed with a rare form of motor neurone disease.
The illness left him wheelchair-bound and largely unable to speak except through a voice synthesiser.
In a statement his children, Lucy, Robert and Tim, said: “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.”
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
Published his book A Brief History of Time in 1988, which has sold more than 10 million copies
His life story was the subject of the 2014 film The Theory of Everything, starring Eddie Redmayne
The scientist gained popularity outside the academic world and appeared in several TV shows including The Simpsons, Red Dwarf and The Big Bang Theory.
He was portrayed in both TV and film – recently by Eddie Redmayne in the film The Theory of Everything which charted his rise to fame and relationship with his first wife Jane.