The musician died from kidney failure at the age of 62 on May 20. He had previously battled colon and liver cancer.
His son Robin-John Gibb told The Sun: "When he passed away we went out [of the hospital room], [the medical staff] took the equipment away and we came back in. I picked up my phone and found 'I Started A Joke' on YouTube and played it.
"I put the phone on his chest and that was the first time I broke down. I knew that song and its lyrics were perfect for that moment. That song will always have new meaning to me now."
RJ went on to reveal that it has been hard to hear the track since his father's passing.
He added: "A couple of days later I was at our favourite restaurant and 'I Started A Joke' came on the radio the exact time he died, 10.46pm.
"I cried that time too, but in a different way. If you listen to the lyrics, 'I finally died, which started the whole world living', that goes with dad's spirit that the show must go on. It will definitely be played at the funeral."
A private memorial ceremony will be held for family and friends in Thame, Oxfordshire on June 8.
Watch The Bee Gees perform 'I Started A Joke' below: