Graham Jenkins, who lived in Cwmafan, Port Talbot, died in his sleep aged 88 after being diagnosed with Alzheimer's Disease a number of years ago.
He was the youngest of the 13 children born to Burton's mother, Edith Jenkins. She died soon after he was born.
Mr Jenkins is survived by his wife Hilary, 86, and two sons Richard and Alun.
His funeral will be held at Margam Crematorium on Thursday.
Mr Jenkins's niece Sian Owen said: "We've had comments whether the crematorium will be big enough for the funeral.
"He was brilliant, kind hearted, a real gent."
Burton's daughter, Kate, is among those who will attend the funeral.
After the death of his mother, Mr Jenkins was brought up by one of his brothers, while Richard, who was the 12th-born child, was raised by his sister.
Mr Jenkins had worked as a market inspector in Port Talbot, manager of Afan Lido, and latterly as a sports organiser for the BBC in London.
He had also lived in Guernsey before moving back to south Wales.
On a local website, Mr Jenkins recalled competing against his famous brother in the Eisteddfod: "Rich won, even though I was told I had the sweeter voice, however Rich had the stage presence.
"I cried over this and Rich kindly shared his winnings with me.  "
He also wrote that he acted as a stage double for Burton, adding, "at one time I had to kiss Elizabeth Taylor".
Burton, who was famously married twice to film star Taylor, died in 1984.
The last surviving brother of the late Hollywood actor Richard Burton has died, his family has confirmed.