Redmayne, who played the role of the professor in the 2014 biographical drama The Theory of Everything, was seen arriving at the church earlier.
He is due to read Ecclesiastes 3.1-11, while eulogies will be delivered by Robert Hawking and Prof Dowker.
The service will be officiated by the Reverend Dr Cally Hammond, Dean of Gonville and Caius College, where Prof Hawking was a fellow for more than 50 years.
Obituary: Stephen HawkingStephen Hawking: A life in picturesCambridge remembers Stephen Hawking Image copyright Sir Cam Image caption People have gathered outside the church waiting for the funeral cortege to arrive The church bell will toll 76 times - once for each year of Prof Hawking's life, when the funeral cortege arrives.
An arrangement of white lilies, to represent the universe, and another of white representing the polar star will be placed on top of his coffin.
His ashes will be interred next to the grave of Sir Isaac Newton at Westminster Abbey in June.
Although the professor's funeral is private, people have begun gathering in the centre of Cambridge to witness the arrival of the funeral cortege on Saturday afternoon.
Image copyright Dan White Image caption The professor was photographed clutching his college's teddy bear mascot While no full road closures are planned, traffic will be held briefly in parts of Cambridge as the funeral cortege passes from the professor's home in the west of the city to King's Parade and the area around Great St Mary's Church.
There is likely to be increased congestion, the university has said.
A condolence book, which was opened on the morning of Prof Hawking's death, will be available to members of the public in the porters' lodge of Gonville and Caius College.
Image copyright BBC/Richard Ansett You may also be interested in:
Pupils 'should revise 7 hours a day' over Easter Camera rescued after two years lost at sea Church sign proclaims 'Chris is Risen'