The actor, who won an Oscar for his portrayal of Professor Hawking in the 2014 biopic The Theory of Everything, gave a reading at the private service, attended by 500 guests.
The biblical text ended with the lines: “I have seen the business that God has given to the sons of men to be busy with.
“He has made everything beautiful in its time; also he has put eternity into man’s mind.”
Professor Hawking’s children, Tim, Robert and Lucy, were among those at the service, along with celebrities including model Lily Cole, Queen guitarist Brian May and comedian Dara O Briain, who made a documentary about the physicist.
SpaceX CEO Elon Musk and playwright Alan Bennett were on the guest list, while Astronomer Royal Martin Rees also spoke during the service.
Professor Hawking died peacefully in his sleep earlier this month aged 76.
Prior to the funeral, hundreds of people lined the streets around the University Church of St Mary the Great, near to Gonville and Caius College where Prof Hawking was a fellow for 52 years.
The watching crowd broke into spontaneous applause as Professor Hawking’s coffin, topped with white “Universe” lilies and white “Polar Star” roses and carried by porters from the University of Cambridge, was taken into the church.
The church bell had tolled 76 times, once for each year of the physicist’s life, as the hearse arrived outside the church, while the colleges’ flags flew at half mast in his honour.
The Gonville and Caius College choir sang Beyond The Night Sky, a song the college commissioned as a gift for Professor Hawking for his 75th birthday last year.
Its lyrics include quotes from A Brief History of Time, which especially pleased Professor Hawking, who said of the song: “It takes us all on a mental journey around the universe.”
The physicist, born in Oxford in 1942, was 21 years old when he was diagnosed with motor neurone disease in 1963 and given just two years to live.
He was forced into a wheelchair by the debilitating disease, and, as his condition worsened, had to resort to speaking through a voice synthesizer and communicating by moving his eyebrows.
Undaunted, he went on to study cosmology at Cambridge and became one of the most brilliant theoretical physicists since Albert Einstein.
His 1988 book A Brief History Of Time sold 10m copies and was translated into 35 languages.
Prof Hawking’s ashes will be interred close to the remains of Sir Isaac Newton in Westminster Abbey in June.