Eddie Redmayne, who played the professor in 2014’s The Theory of Everything, was among 500 guests invited to the University Church of St Mary the Great.
He gave a biblical reading at the service, and astronomer Royal Martin Rees also spoke.
Model Lily Cole, Queen guitarist and astrophysicist Brian May and comedian Dara O Briain were among those seen arriving tothe funeral.
The church bell tolled 76 times, once for each year of Prof Hawking’s life, as the solid oak coffin adorned with floral tributes arrived in a hearse.
A round of applause spontaneously broke out as Prof Hawking’s coffin was carried into the church by six porters from Cambridge University’s Gonville and Caius College, where he was a fellow for 52 years.
Family members of the cosmologist, including his three children a Lucy, Robert and Tim, followed the coffin into the church.
In a statement released ahead of Saturday’s service they said they chose to hold the funeral “in the city that he loved so much and which loved him”.