The English physicist died peacefully at his home in Cambridge in the early hours of the morning.
"He was a great scientist and an extraordinary man whose work and legacy will live on for many years", Hawking's children, Lucy, Robert and Tim, said in a statement.
"His courage and persistence with his brilliance and humour inspired people across the world", the family said.
"This complete set of laws can give us the answers to questions like how did the universe begin", he said.
Most of Hawking's life was spent in a wheelchair, crippled by amyotrophic lateral sclerosis (ALS), a form of motor neuron disease.
The best-known theoretical physicist of his time, Hawking wrote so lucidly of the mysteries of space, time and black holes that his book, "A Brief History of Time", became an worldwide bestseller, making him one of science's biggest celebrities since Albert Einstein.
The illness gradually robbed him of mobility, leaving him confined to a wheelchair, nearly completely paralysed and unable to speak except through his trademark voice synthesiser.More news: SP leads in Gorakhpur, Phulpur bypolls
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One of Hawking's former students at Cambridge, theoretical physicist Raphael Bousso, told Nature that his teacher was a brilliant physicist who also excelled at communicating science to the public.
Professor Stephen Hawking speaks during the Opening Ceremony of the London 2012 Paralympics at the Olympic Stadium on August 29, 2012 in London, England.
At Cambridge, he held the position of Lucasian Professor of Mathematics - the prestigious post held from 1669 to 1702 by Sir Isaac Newton, widely considered one of the greatest scientists in modern history.
In an exclusive interview with CNN in October 2008, Hawking said that if humans can survive the next 200 years and learn to live in space, then our future will be bright. Hawking authored seven books, co-authored nine others, and was the recipient of dozens of scientific, academic, and other awards including The Albert Einstein Award, The Hughes Medal, and the Presidential Medal of Freedom.
Hawking's seminal contributions continued through the 1980s.
He also appeared as himself in an episode of the BBC comedy series, Red Dwarf and as a hologram of his image in Star Trek: The Next Generation.
In 2015, British actor Eddie Redmayne won an Oscar for his portrayal of Prof Hawking in the biopic The Theory of Everything the previous year.
American astrophysisist Neil deGrasse Tyson wrote: "His passing has left an intellectual vacuum in his wake. Think of it as a kind of vacuum energy permeating the fabric of spacetime that defies measure". "We have lost an awesome human being".