The Bee Gees star was thought to have passed away on May 20 as a result of colon and liver cancer, which he had been battling for some time.
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"The end was peaceful and dignified, there were no theatrics. It was only later that I cried and cried," RJ told the Sunday Express, "It wasn't the cancer that killed my father; those reports are wrong.
"Dad had actually gone into remission and the cancer was completely unrecognisable, it was too small to detect. No scan could see it. He actually died of kidney failure.
"Three days before, he was sitting up and watching DVDs and then suddenly he had a seizure. He was then dosed with sedatives to deal with the side effects of his chemotherapy and his liver just couldn't process them."
RJ also revealed the family's plans for the singer's funeral.
"We've been discussing hymns and songs," he said. "There will be some Bee Gee tracks, though we don't know which yet, and maybe Roy Orbison's 'Crying'. My father loved Roy's music and they were great friends."
Barry Gibb recently released a video montage in tribute to his late brother.
Photo gallery - Robin Gibb's career in pictures:
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