One thousand members of the public, from more than 100 countries, were offered the opportunity to attend the service, after a ballot attracted 25,000 applications for tickets.
A private funeral service was held in March in Cambridge, where Hawking lived and worked for decades.
Prayers were led by the Reverend Mark Birch, minor canon and sacrist, and said by the Reverend Dr Cally Hammond, dean of Gonville & Caius College, his ex-wife Jane Hawking, Elinor Tatum, University of Cambridge vice-chancellor Professor Stephen J Toope OC, and the Reverend Jane Sinclair, canon in residence.
Hawking was also a pop culture icon, appearing in several TV series playing himself, including "Star Trek: The Next Generation" and American cartoon sitcom "The Simpsons".
An address will be given by Astronomer Royal Martin Rees, while Prof Hawking's collaborator and Nobel prize victor Kip Thorne will give a tribute.
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