There were also tributes from Astronomer Royal Martin Rees and Nobel prize victor Kip Thorne.
Labour leader Jeremy Corbyn, musician Nile Rodgers, TV star David Walliams and Professor Brian Cox were among the guests who gathered to remember the renowned physicist.
One thousand members of the public from more than 100 countries, including some in wheelchairs, attended Friday's ceremony, after a ballot attracted over 25,000 applications for tickets.
The scientist has taken his place among Britain's greatest with the burial of his ashes in Westminster Abbey, between the graves of Charles darwin and Isaac Newton.
Hawking's cremated remains were placed in the 900-year-old abbey's so-called "Scientists' Corner", a section dedicated to the United Kingdom's most groundbreaking scientists, including Michael Faraday who discovered electromagnetic induction and inventor of the electric dynamo, and James Clerk Maxwell who formulated the classical theory of electromagnetic radiation. He spent his life probing the origins of the universe, the mysteries of black holes and the nature of time itself.
Actor Benedict Cumberbatch, who played Hawking in a 2004 BBC biopic, and British astronaut Tim Peake, were among those who gave readings at the service. The memorial is inscribed with his most famous black hole equation, hovering over a series of rings.
Rees, who first met Prof Hawking at the University of Cambridge in the early 60s, paid tribute to the scientist's great contributions to the world.
Professor Hawking's daughter, Lucy, said the music would be aimed at "the nearest black hole, 1A 0620-00".
The physicist's voice will also be sent into space by the European Space Agency. "It is a message of peace and hope, about unity and the need for us to live together in harmony on this planet".
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.
Hawking's place in Westminster Abbey displays a stone that says, "Here lies what was mortal of Stephen Hawking", which is the English translation of the Latin words displayed in Newton's grave. An address was given by Astronomer Royal Martin Rees, who first met Prof Hawking at the University of Cambridge in the early '60s, while Prof Hawking's collaborator and Nobel prize victor Kip Thorne also gave a tribute.
Greek composer Vangelis - yes, the "Chariots of Fire" guy - set the physicist's voice to an original piece of music for the occasion.
At the same time when Hawking's ashes were laid to rest at the Westminster Abbey, the ESA beamed the scientist's distinctively synthesized voice towards the closest-known black hole.
In 1986, he wrote "A Brief History of Time", an global bestseller which made him one of the most prominent names in science since Albert Einstein.
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