The singer admits he grew apart from his sibling in recent years, and barely spent any time with him before his death from cancer in 2012.
Gibb has now revealed he had no idea Robin's condition was so serious until he saw his picture in a newspaper.
He tells Britain's Daily Mail, "I didn't realise Robin was seriously ill for about a year, when I began to see the pictures of him in the paper. I thought something's wrong here - but I couldn't get any answers out of anyone.
"No one called from his house. I'd probably do the same thing - who wants to be thought of as an invalid? I don't think they knew how serious it was going to become, but I think they knew two years before, or a year at least, before I knew.
"Dwina (Robin's wife) started to tell us things gradually, and about six months before Robin passed she began to be very open with us. We were hearing stories: the fact he didn't want to go into hospital, that he didn't want to have chemo. All the signs that you know something's really wrong."
Gibb, who lives in America, took a newspaper cutting to his doctor to ask his opinion on his brother's health and was told he should fly back to his native Britain to visit as soon as possible.
He adds, "I showed my doctor in Miami a newspaper picture of Robin and he took one look and said: 'You've got to go and see your brother.' I asked him for a prognosis because no one in England would give me one, and he said: 'Three to six months. Go as soon as you can.'
"We flew over to see him. He was extremely weak but he seemed Ok otherwise. We laughed about a lot of things and we sort of made up. At least we were together, and we were talking to each other and laughing."
Gibb also reveals he later visited his brother after he had slipped into a coma, and sang to him while he was unconscious.
He wrote the song, titled The End of the Rainbow, especially for Robin and intends to include it on his next album.