He died peacefully at his home in Cambridge in the early hours of Wednesday, his family said.
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.
Prof Hawking was the first to set out a theory of cosmology as a union of relativity and quantum mechanics.
He also discovered that black holes leak energy and fade to nothing - a phenomenon that would later become known as Hawking radiation.
Tributes are pouring in for famed physicist and author Stephen Hawking who passed away at the age of 76.
Actor Eddie Redmayne, who won an Oscar for portraying Hawking in the movie The Theory of Everything, said, "We have lost a truly beautiful mind, an astonishing scientist and the funniest man I have ever had the pleasure to meet. My love and thoughts are with his extraordinary family." The cast of TV's The Big Bang Theory, who often referenced Hawking on the show and even welcomed him as a guest star in one episode, tweeted, "In loving memory of Stephen Hawking. It was an honor to have him on The #BigBangTheory. Thank you for inspiring us and the world."
The show's star, Kaley Cuoco, separately wrote on Instagram, "It was truly such an honor getting to work with the incredible Stephen Hawking. He made us laugh and we made him laugh. His life and career workings have been many a subject matter on @thebigbangtheory and we are all better for it."
Here are some other tributes:
Neil deGrasse Tyson: "His passing has left an intellectual vacuum in his wake. But it's not empty. Think of it as a kind of vacuum energy permeating the fabric of spacetime that defies measure. Stephen Hawking, RIP 1942-2018."
Katy Perry: "There’s a big black hole in my heart hours before Pi day. Rest In Peace @Steven_Hawking."
Kumail Nanjiani: "RIP Stephen Hawking. Genuinely very sad to hear that. If you haven’t, read A Brief History of Time. It’ll make the world feel more amazing and beautiful and strange. It’ll also make you feel smart and stupid all at once."
Mira Sorvino: "I am very saddened to hear of Stephen Hawking’s passing. His book was an enormous influence on me in college and meeting and getting to talk with him was one of the great thrills of my life. You are shining in the heavens you so loved now!"
Zoe Saldana: "Farewell to a brilliant mind. Thank you for being so generous with your knowledge in the brief time you were with us."
Larry King: "I once asked Stephen Hawking in an interview what puzzles him the most in all the universe. 'Women,' he answered. He will be missed. R.I.P."
British PM Thersa May: "Professor Stephen Hawking was a brilliant and extraordinary mind - one of the great scientists of his generation. His courage, humor and determination to get the most from life was an inspiration. His legacy will not be forgotten."