The ceremony for the renowned British physicist will be carried out during a thanksgiving service later this year, a spokesman for the abbey said.
Hawking – regarded as one of the world’s finest scientific minds – died last week at the age of 76.
He died peacefully at his home in Cambridge in the early hours of Wednesday morning.
The Dean of Westminster, the Very Reverend Dr John Hall, said: “It is entirely fitting that the remains of Professor Stephen Hawking are to be buried in the Abbey, near those of distinguished fellow scientists.
“Sir Isaac Newton was buried in the Abbey in 1727.
“Charles Darwin was buried beside Isaac Newton in 1882.
“Other famous scientists are buried or memorialised nearby, the most recent burials being those of atomic physicists Ernest Rutherford in 1937 and Joseph John Thomson in 1940.
“We believe it to be vital that science and religion work together to seek to answer the great questions of the mystery of life and of the universe.”
In a statement, his children Lucy, Robert and Tim had said: “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.
“His courage and persistence with his brilliance and humour 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.”
Prof Hawking was born on 8 January 1942 in Oxford – the eldest of four children – and went on to become one of the world’s most acclaimed cosmologists.
He was diagnosed with ALS – a rare form of motor neurone disease – in his 20s, eventually becoming wheelchair-bound and dependent on a computerised voice system for communication.
But despite this, he continued to travel the world giving science lectures and writing scientific papers about the basic laws which govern the universe.
With Roger Penrose, he showed Einstein’s General Theory of Relativity implies space and time would have a beginning in the Big Bang and an end in black holes.
These results indicated it was necessary to unify general relativity with quantum mechanics, the other great scientific development of the first half of the 20th century.
He also discovered that black holes should not be completely black, but rather should emit radiation and eventually evaporate and disappear - this radiation is now called Hawking Radiation.
His book, A Brief History Of Time, has sold more than 10 million copies.
Eddie Redmayne led tributes to Prof Hawking, describing him as “the funniest man” he has ever met.
The actor, who won an Oscar for his portrayal of Prof Hawking in 2014 film The Theory Of Everything, said in a statement: “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.”
Prime Minister Theresa May was among others paying tribute to Prof Hawking.
She said: “Professor Stephen Hawking was a brilliant and extraordinary mind - one of the great scientists of his generation.
“His courage, humour and determination to get the most from life was an inspiration. His legacy will not be forgotten.”
Scientist and broadcaster Professor Brian Cox told BBC Radio 4’s Today programme that Prof Hawking was “one of the greats”.
“There are many good theoretical physicists who make a big contribution, but there aren’t that many greats,” he added.
“And by that I mean that I think there are physicists in a thousand years’ time, they will still be talking about Hawking radiation, they will be using his fundamental results on black holes.
“Actually, the last time I saw him at his 75th birthday party, he was talking about the new gravitational wave experiment where we’ve seen the collisions of black holes, and speculating that those results might be able to prove some of his theorems once and for all.
“Plus his contributions to the physics of the very early universe, so there are at least three and possibly more areas where his work will be remembered as long as there are cosmologists and that’s the best you can hope for as a scientist.”
The University of Cambridge, where Professor Hawking studied and worked, will open a book of condolence at Gonville and Caius College.
University of Cambridge vice-chancellor Professor Stephen Toope said: “Prof Hawking was a unique individual who will be remembered with warmth and affection not only in Cambridge but all over the world. His exceptional contributions to scientific knowledge and the popularisation of science and mathematics have left an indelible legacy. His character was an inspiration to millions.”
NASA remembered Prof Hawking as a “renowned physicist and ambassador of science”.
“His theories unlocked a universe of possibilities that we & the world are exploring. May you keep flying like superman in microgravity, as you said to astronauts on @Space_Station in 2014,” the organisation tweeted.
Indian prime minister Narendra Modi said Prof Hawking had “made the world a better place” and his death was “anguishing”.
“Professor Stephen Hawking was an outstanding scientist and academic. His grit and tenacity inspired people all over the world,” a tweet on his page said.
US astrophysicist Neil deGrasse Tyson was one of the first to pay tribute to Prof Hawking.
Sharing a photo of himself and Prof Hawking on Twitter, he said the scientist’s death had “left an intellectual vacuum in his wake”.
He added: “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.”
Sean Carroll, a physics professor at US university Caltech, said: “Stephen Hawking was the rare famous scientist who deserved every bit of his fame. A brilliant physicist and an inspirational person. And quite a character.”
Greenpeace USA thanked Prof Hawking for helping people understand their place in the universe and for “leaving us in awe and wonder”.
Celebrities also paid tribute, with US singer Katy Perry saying his death left a “big black hole in my heart”.
Jonathan Ross tweeted: “RIP Stephen Hawking. The world just dropped a lot of IQ points. And, he was a fun person. Very sad news.”
KT Tunstall tweeted: “Wow. What a life. What an extraordinary Human Being. Enjoy the cosmos Stephen Hawking, the biggest and most mysterious adventure that we all get to go on one day... RIP #genius.”
The rock band Foo Fighters tweeted: “’Remember to look up at the stars and not down at your feet’ - RIP Stephen Hawking you f****** legend.”
US actor Macaulay Culkin described Prof Hawking as a “genius”, adding that the physicist was also his favourite Simpsons character.
He tweeted: “I just heard about Stephen Hawking’s passing. He was both a genius and my favorite Simpsons character. We’ll miss you, buddy.”
Defence Minister Tobias Ellwood said Prof Hawking “epitomised true courage over adversity as you explained the wonders of the universe to the world”.
He wrote on Twitter: “Your achievements symbolise the pwr of the human mind. An inspiration to us all, whatever our station in life, to reach for the stars-from where you now shine down on us.”