Gibb, 62, awoke from a days-long coma during the weekend.
His wife, Dwina Murphy-Gibb, told ITV News Tuesday her husband was "really happy" and "just wants to get out" of The London Clinic and go home.
"They gave him an under 10 percent survival chance and he has beaten the odds," Gibb's son, Robin-John, said. "He really is something else."
The BBC said Gibb's family, including his son, Spencer, and daughter Melissa, kept a bedside vigil, talking to and playing music for the ailing former Bee Gees member.
Robin-John told ITV two days before his father came out of the coma, "they said they had thrown the kitchen sink at him, that it was time to make plans because he was in God's hands."
The elder Gibb's physician, Dr. Andrew Thillainayagam, said in a statement posted on the musician's Web site Monday, "The road ahead for Robin remains uncertain but it is a privilege to look after such an extraordinary human being."