The Bee Gees star - who has liver and colon cancer - was thought to be very close to death after contracting pneumonia and slipping into a coma last week, but he has since made startling progress.
The 'How Deep is Your Love' singer's wife Dwina was even told by doctors at The London Clinic in central London he only had days to live, but Robin is now awake, breathing with an oxygen mask and able to talk with friends and relatives.
Dr Andrew Thillainayagam of Imperial College, London, said: "The prognosis was very grave. We felt it was very likely Robin would succumb to what seemed to be insurmountable obstacles.
"It is testament to Robin's extraordinary courage, iron will and deep reserves of physical strength that he has overcome quite incredible odds.
"Robin is fully conscious, lucid and able to speak to his loved ones. He is breathing on his own.
"He is on intravenous feeding and antibiotics. He is of course, exhausted, extremely weak and malnourished."
The doctor added he was hoping that with further progress Robin could be moved from the intensive care unit of the hospital to the ward and begin the process of nutritional and physical rehabilitation.
He also praised Dwina and the couple's children Robin-John, Spencer and Melissa for their "determination never to give up on him."
Robin's family held a constant bedside vigil for him and played his favorite music to encourage him.
Robin's brother and Bee Gees band mate, Barry, 65, had also been singing to him.
Dwina has said Robin even cried when she played Roy Orbison's track 'Crying'.