Hawking's children, Lucy, Robert and Tim, said in a statement: " We are deeply saddened that our beloved father passed away today.
"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 humor" 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."
Hawking was driven to Wagner, but not the bottle, when he was diagnosed with motor neurone disease in 1963 at the age of 21. Doctors expected him to live for only two more years. But Hawking had a form of the disease that progressed more slowly than usual. He survived for more than half a century.
Those who live in the shadow of death are often those who live most. For Hawking, the early diagnosis of his terminal disease, and witnessing the death from leukaemia of a boy he knew in hospital, ignited a fresh sense of purpose. “Although there was a cloud hanging over my future, I found, to my surprise, that I was enjoying life in the present more than before. I began to make progress with my research,” he once said. Embarking on his career in earnest, he declared: “My goal is simple. It is a complete understanding of the universe, why it is as it is and why it exists at all.”
Hawking was a fun loving guy. Inside that shell, inside that body that was paralysed, was someone who was full of vigour, full of passion for life.
Mr Hawking is an example great person who I often write articles when I was at school. He is one of the most amazing person I have known.
"A star just went out in the cosmos," tweeted Lawrence Krauss, a theoretical physicist and cosmologist. "We have lost an amazing human being.
Now we have lost an amazing human being.