He died peacefully at his home in Cambridge in the early hours of this morning.
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.
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, say they are deeply saddened.
They call him a great scientist and an extraordinary man whose work and legacy will live on for many years.