With celebrities and science enthusiasts from around the world in attendance, the ashes of the theoretical physicist were interred by the graves of fellow science greats Isaac Newton and Charles Darwin.

A specially-written musical piece by Greek composer Vangelis featuring Hawking's famous synthesized voice was beamed into space by radio waves from a European Space Agency satellite dish in Spain.

The ESA said the six-minute message, drawn from a speech Hawking gave about preserving the planet, was being transmitted towards the black hole 1A 0620-00, which was discovered in 1975 and is located 3,500 light years from Earth.

"This is a beautiful and symbolic gesture that creates a link between our father's presence on this planet, his wish to go into space and his explorations of the universe in his mind," said his daughter Lucy Hawking.

"It is a message of peace and hope, about unity and the need for us to live together in harmony on this planet," she said.

- Most famous equation -

Hawking, who was wheelchair bound due to motor neurone disease, dedicated his life's work to unraveling the mysteries of the universe and fought to overcome his disability.

Although Hawking was an avowed atheist, Friday's service was nonetheless held at London's giant Westminster Abbey to accommodate large numbers of family, friends and colleagues.

The memorial stone on top of Hawking's grave included his most famous equation describing the entropy of a black hole.

"Here Lies What Was Mortal Of Stephen Hawking," read the inscription on the stone, which included an image of a black hole.

Hawking, who captured the imagination of millions around the world, died on March 14 at the age of 76.

Read also: UK to offer Stephen Hawking fellowships

Propelled to stardom by his 1988 book "A Brief History of Time", an unlikely worldwide bestseller, Hawking's genius and wit won over fans from far beyond the rarefied world of astrophysics.

His death triggered a flood of tributes from Queen Elizabeth II to NASA, reflecting his impact as a scientist but also a beacon of hope for people affected by motor neurone disease.

It celebrated not only his achievements as a scientist, but also his character and endurance living with a devastating illness.

"We are so grateful to Westminster Abbey for offering us the privilege of a service of thanksgiving for the extraordinary life of our father and for giving him such a distinguished final resting place," said his children Lucy, Robert and Tim.

Around 1,000 members of the public drawn from more than 100 countries attended the service, following an online ballot in which 25,000 applied for tickets.

Applicants needed to give their birth date -- but eagle-eyed fans spotted that it could be any day up to December 31, 2038, opening the door to time-traveling guests from the future.

Mourners were welcomed by volunteers from the London 2012 Paralympic Games opening ceremony, in which Hawking starred.

British astronaut Tim Peake, astronomer royal Martin Rees, and actor Benedict Cumberbatch, who played Hawking in a television film and narrated his documentaries, delivered addresses.

Three young people who use electronic communication devices to speak, just as Hawking did, were also among the guests.

Jason Felce, 20, who controls his equipment with eye movement, said: "He has inspired me to be the best that I can be and not let anything, including my disability, hold me back".

Jim Trevino, a self-described "student of science", who came from Las Vegas for the ceremony, said the service was "spectacular".

"It was a combination of the sacred and the profane, of science and religion."

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