The 24 year-old's funeral was preceded by a memorial service at Holy Trinity Church attended by family and friends.
Mr Miller was murdered on the island of Koh Tao with fellow traveller Hannah Witheridge, 23, of Hemsby, Norfolk, on 15 September.
Two suspects from Myanmar have been arrested by Thai police, who say the pair have confessed.
Friends and family of Mr Miller paid tribute and sang hymns during the afternoon before the family held a private funeral ceremony elsewhere.
Mr Miller was carried in a wicker coffin adorned with sunflowers.
The memorial service, led by Reverend Ian Pallent, also included a performance of Bob Dylan's song Forever Young.
Mr Pallent told BBC News: "David was such a colourful character; a man of life, energy and vitality.
"Whilst there is great sadness that someone so young has died, this is about a celebration of his life, to give thanks to God for the impact he made.
"What we will do today and all through the next few months is show love: love to his parents, to his brother, all his friends and the rest of his family."
In a statement on Wednesday, Mr Miller's family said he "brightened up their world" and they would miss him terribly.
Mr Miller worked as an intern in the St Helier offices of Australian mining company Consolidated Minerals.
He was returning from a placement in Australia when he stopped off in Thailand for a holiday.
The funeral of David Miller, the Jersey islander murdered in Thailand, has taken place on the island.