Robin lived in Thame for many years and died from kidney failure on May 20th after suffering from cancer and pneumonia. He was burried June 8th.
Thousands of fans lined the streets of Thame as a lone bagpiper led a procession through the town.
Robin and Dwina's home, a converted 13th century monastery, is opposite the church but the carriage travelled along the market town's high street first as it was among Robin's last wishes that he could 'say a final goodbye to fans and his home town'.
The decorative carriage left from Priests End in the town at around 1.30pm and travelled along the High Street to St Mary's Church, where the ceremony took place.
Onlookers watched the white, glass-sided carriage - topped with red roses and pulled by four plumed, black Friesian horses. In keeping with his long musical career, the horses wore decorative black cloths emblazoned with a gold treble clef and were accompanied by a piper.
The casket was draped with the flag of the Isle of Man, where the brothers were born.
Joining funeral directors as pallbearers were Gibb's sons RJ and Spencer, together with Stevie Gibb, Barry's son, and Steven Murphy.
a last goodbye to Thame and to Rob's fans
Uniformed cadets from 594 Thame Squadron of the Air Training Corps also lined up outside the church to honour Robin Gibbs' campaign for a memorial to members of Royal Air Force Bomber Command who were killed in action.
The stone monument to Bomber Command, a key element of Britain's forces in World War II, has been completed in Hyde Park in London but Robin did not survive to see it unveiled later this month
(June 28th.) by Queen Elizabeth the 2nd. She will be joined by other royals. (expected to be Prince Phillip, Prince Charles and Camilla and Prince Andrew).
The horse-drawn carriage was followed by Robin and Dwina's two Irish wolfhounds, close family and many guests, including broadcaster Paul Gambaccini, actor Leslie Phillips,
Mike Read, West End composer Tim Rice, Susan George and Uri Geller.
The horse-drawn carriage passed through the town prior to the private church service.
Barry Gibb and the vicar leading the service, the Reverend Alan Garratt, walked up the aisle ahead of it as a round of spontaneous applause broke out from well-wishers outside the church.
Close relatives, including Robin's widow, Dwina, and his mother, Barbara, followed behind. Barbara left the church just before Barry, the last of the four Gibb brothers, gave his eulogy.
Grieving Barry spoke movingly of the day the legendary band will reform beyond the grave and read out a poem he had written called: Ode To Rob.
Its emotional lines included the words: "We will all be together one day. So fly away, Rob, fly away. But knowing Rob, he will always be near.
You will always be with us. I love you Rob and always will."
Barry told the congregation: "This is a very strange experience, having already lost two brothers and now Rob. "I think there are an awful lot of things happening right now that maybe you won't be aware of. And one is how many people came on such a terrible day. It is staggering.
Barry said in his eulogy that the death of twin Maurice Gibb in 2003 had hit Robin hard. He told guests at St Mary's Church opposite the home Robin and Dwina had shared for nearly 20 years:
"They were both beautiful. And now they're together. They're actually together. When you're twins, you're twins all your life. You go through every emotion.
I think the greatest pain for Robin in the past 10 years was losing his twin brother, and I think it did all kinds of things to him.
And now they're together. Life is too short. In Robin's case, absolutely too short.
left: the coffin enters the church right: Robin's beloved Irish wolfhounds
"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."
He also spoke about his brother's family and Robin's love for his children Spencer, Melissa, RJ. and little Snow.
Barry also hinted at recent tensions between himself and Robin saying: "We were laughing all the way. Sometimes crying. God knows how much we argued.
"Even right up to the end we found conflict with each other, which now means nothing. It just means nothing. If there's conflict in your lives: get rid of it."
He said their favourite television programme was The Goons, and added: "There was no funnier man than Spike Milligan, apart from Robin. And his sharp, intuitive wit will live with us forever.
"You could stand Robin next to Spike Milligan and it would be a competition." How Deep Is Your Love, Don't Cry Alone and I Started A Joke were played during the service.
Son RJ said of his father: "I will love you always and will take comfort that you are always only a song away, as I will surely hear your voice wherever I go."
Daughter Melissa was too emotional. Her tribute therefore had to be read for her by brother Spencer. It said: "How brave you are. You are a special angel."
In Spencer's eulogy he said: "I will always be humbled by my father's voice and talent."
Radio presenter Henry Wymbs friend of the family: "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."
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."
After the service guests filed out of the church to the sound of the Bee Gees' song " I Started A Joke," which includes the line: "Till I finally died, which started the whole world living."
Robin was then buried in the churchyard, with a piper playing " Ellan Vannin," the unofficial anthem of the Isle of Man, where the Bee Gees were born. Mourners tossed red roses into the grave.
Wreaths at the grave side included a treble clef and music notes formed of red roses, each with a personal note from family members.
Though it was very windy, thankfully, the rain kept off and there was a glimmer of sunshine during Robin's interment.
Once the illustrious guests, the fans and well-wishers, the TV Outside Broadcast vans and all the paparazzi had gone away,
Thame was able to return to normal life. But the town will never be quite the same again without its very own resident mega star, who leaves behind a musical legacy that will live on for generations.
As a banner hanging in the window of the Italian restaurant in the town, Mia Capri said: "Ciao Robin."
The service of June 8th. was just for family and close friends. A public memorial will be staged in London in September.
Robin's wife Dwina read a poem of her own composition at the service
click here (Pdf) to read the poem.