Warren, 79, who started the Granada Television show when he was 24, died on 1 March after a short illness.
His coffin was carried into the cathedral by members of the cast, watched by the crowds outside.
Among those who attended the service were Julie Goodyear and William Roache, who has played Ken Barlow since the first episode in 1960.
Goodyear, famous for playing barmaid Bet Lynch, paid a heartfelt tribute to Warren, a friend of 50 years.
"We cried together and we laughed together," she said.
Canon Philip Barratt said all the hymns and readings at the funeral, which was also open to members of the public, were chosen by Warren.
"It's a big service for a very big character and a lovely part of the history of Manchester," he said.
Former stars in the congregation included Ken Morley, who played Reg Holdsworth, and Christopher Quinten, best known for his role as mechanic Brian Tilsley.
Warren was born Anthony McVay Simpson in Eccles, Salford, in 1937, and took the stage name of Warren during his career as a child star.
He trained at Liverpool's Elliott Clarke Theatre School and was a regular on the BBC radio show Children's Hour, before acting in radio plays alongside some of the actors who would became household names because of Coronation Street, including Violet Carson and Doris Speed.
His idea for the soap opera was commissioned for 13 episodes by Granada in 1960 and the show has gone on to be one of the UK's most successful ever, reaching viewing figures of 26.6 million for the departure of the much-loved character Hilda Ogden in 1987.
He wrote episodes for the ITV soap until the late 1970s and was made an MBE in 1994 for his services to television drama.
The writer remained a consultant on the soap until his death, with his creator credit appearing at the start of the closing credits of every episode.
The funeral of Coronation Street creator and writer Tony Warren has taken place at Manchester Cathedral.