"His courage and persistence with his brilliance and humour inspired people across the world", his children, Lucy, Robert and Tim said in a statement.
"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 for ever", it said.
"Alongside the benefits, AI will also bring dangers, like powerful autonomous weapons, or new ways for the few to oppress the many", Hawking said in 2016, at the opening of a new AI research centre at Cambridge University.
Hawking's death, according to the AP, was announced by a family spokesperson. Hawking lived with the normally fatal illness for over 50 years.
He went on to become a researcher at the University of Cambridge and Professorial Fellow at the Gonville and Caius College.
Often referred to as "one of the most unread books of all time" for the hard-to-grasp concepts, it included only one equation: E = mc2 or the equivalence of mass and energy, deduced by Einstein from his theory of special relativity.
This process helps explain the notion that black holes have existed at a micro level since the Big Bang, and the smaller they are, the faster they evaporate. As his condition worsened, he had to resort to speaking through a voice synthesiser and communicating by moving his eyebrows.
But the power of his intellect contrasted cruelly with the weakness of his body, ravaged by the wasting motor neurone disease he contracted at the age of 21.
In 1979 he was appointed Lucasian Professor of Mathematics at Cambridge University, where he had moved from Oxford University to study theoretical astronomy and cosmology.
Professor Hawking has 12 honorary degrees, a CBE and was awarded the US Presidential Medal of Freedom in 2009.
"Professor Stephen Hawking is a brilliant man and a mediocre student", Mr. Obama said.
He called the episode "very amusing and now nearly as many people know me through "The Simpsons" as through my science". The couple split after 25 years and he married his former nurse, Elaine Mason, but the union broke down amid allegations, denied by him, of abuse.
The 2014 movie about his life, "The Theory of Everything", was nominated for Best Picture, and Eddie Redmayne, who played Hawking, won the Oscar for Best Actor.