"He died peacefully in his Cambridge home early in the morning,” his family said.
A British scientist famous for his work with black holes and relativity, and has also written several popular science books including "a brief history of time".
At the age of 22, Professor Hawkin was given only a few years to live after being diagnosed with a rare form of motor neuron disease.
The disease left him in a wheelchair and largely could not speak except through a voice synthesizer.
In a statement, his children, Lucy, Robert and Tim, said, "We are deeply saddened that our beloved father passed away today."
He was shown both on television and in the film – played by Oscar winner Eddie Redmane in "the Theory of everything", who showed his growing fame and relationship with his first wife Jane.
The actor gave a tribute to him, saying: "We have lost a truly beautiful mind, amazing scientists and the most ridiculous person I have ever met".
Defense Secretary Tobias Ellwood said Professor Hawking was "an inspiration to all of us, no matter what our station is in life, to achieve the stars."
He tweeted: "RIP Sir. You represented real courage before adversity when you explained the universe to the world. Your achievements symbolize the power of the human mind."
Local government Minister Sajid Javid said, " One of the most inspiring people of my life. A brief history on the earth, the eternity of the stars."
What a wonderful and extraordinary man. A huge loss for the world, not just for our country.