Hundreds of fans lined the streets of Thame earlier as a lone bagpiper led a procession through the town.
Gibb's body was carried in a horse-drawn carriage, followed by two Irish wolfhounds and guests, including his brother Barry and broadcaster Paul Gambaccini.
Gibb, 62, died of kidney failure in May after battling cancer and pneumonia.
The horse-drawn carriage passed through the town prior to a private church service attended by his family and close friends being held.
His family said his wish was to say a "final goodbye" to fans and the town.
Barry Gibb, the only surviving member of the Bee Gees trio, told the congregation in St Mary's Church: "Life is too short. In Robin's case, absolutely too short.
"We should have had 20 years, 30 years of his magnificent mind and his beautiful heart."
Referring to the large turn-out for the funeral procession and service, he said: "So many people loved this boy, so many illustrious people are here that loved him. And that is such a pleasure to witness.
"The three of us have seen a lot of crowds but I've never seen so much love in one crowd as I'm looking at today - for Rob, you know, for the music. And it's an intense experience for me."
Other guests at the service included musician Peter Andre and actor Leslie Phillips.
The track Don't Cry Alone, which was one of Gibb's final compositions from his Titanic Requiem - premiered only weeks before his death - was played at the service.
Radio presenter Henry Wymbs, who has known the Gibb family for a number of years as Robin's wife Dwina was a fan of his Irish Eye programme, said: "Part of my youth died with him because he created so many of the songs I loved.
"He was humble, down to earth, a very genuine man who wasn't affected by fame or wealth.
"Apparently he had really become a part of the community in Thame and I can believe that because he was such a nice man."
Mayor of Thame Nigel Champken-Woods said: "He did switch the Christmas lights on a few years ago and he was happy to sign autographs and talk to people."
Bee Gees fan Jill Horton, who had travelled to Thame from Buckingham, said: "We're big fans, the whole family, right through to my four-year-old granddaughter.
"It was their music that was just so special.
"He was 62 and I'm 61 so I've grown up in that era."
Gibb's musical career began when he formed the Bee Gees with brothers Barry and Maurice in 1958.
The group is among the biggest-selling acts of all time, with hits including Stayin' Alive, How Deep Is Your Love, Massachusetts and Night Fever.
They made almost 30 albums and sold more than 110 million records.
Their 1977 soundtrack to the film Saturday Night Fever sold more than 40 million copies worldwide, making it the best-selling movie soundtrack of all time.