The track, called Sydney, prompted tears from Gibb and his wife Dwina when he wrote it as he nostalgically looked back at his early life in Australia with his hitmaking brothers.
It was recorded in August 2011, just nine months before his death after a lengthy period of ill health.
Other songs from the album, called 50 St Cathereine's Drive, were recorded between 2006 and 2008 and feature many autobiographical recollections,.
His widow Dwina, who compiled the tracks with son RJ, said: "Robin composed this late at night, in August 2011, at our home, The Prebendal. He used the bedroom keyboards and then Garageband on an I-Pad.
"He wished to finish this song in a studio with Barry, for a new album he hoped they would record together, but his health prevented this. He missed his twin brother Maurice who had passed away; but when he closed his eyes, the three young brothers were back in Sydney, Australia, happy together with their dreams and hopes for the future.
"Their future creations of course affected the world. This fragment of song is poignant, wistful, beautiful and unfinished. It belongs on this album as one of his last works. He cried when he wrote it, and I wept when I heard it."
The album, named after the address of the home in which he was born on the Isle Of Man, is due out on September 29. It will also feature a new version of the Bee Gees song I Am The World.