Celine Dion, who performed with Gibb and his brothers Barry and Maurice on her 1998 track Immortality, said she was "very sad" to hear of his passing.
The Who's Roger Daltrey said Gibb was "a lovely, lovely guy", while Labour leader Ed Miliband said he would be "remembered for his incredible gifts".
Flowers were left on the Bee Gees' star on the Hollywood Walk of Fame in LA.
Floral tributes were also placed by fans outside his home in Thame, Oxfordshire.
Daltrey praised the sensitivity of Gibb's vocals. "I hear everyone talking about the success of their career but I haven't heard many talk about him as a singer and I used to think he was one of the best," he said.
"To me, singing is about moving people and Robin's voice had something about it that could move me and, I'm sure, millions of others. It was almost like his heart was on the outside."
John Travolta, whose film Saturday Night Fever was given a memorable soundtrack by The Bee Gees, said: "I thought Robin was one of the most wonderful people - gifted, generous and a real friend to everyone he knew. And we'll miss him."
Gibb has also been remembered by charities he worked with, such as the Stoke-on-Trent based Cauldwell Children, which helps terminally ill youngsters and their families.
Charity chief executive Trudi Beswick said: "Over the last 18 months we have had the pleasure of working with Robin on several occasions. He was an extremely caring and compassionate person who dedicated much of his time to helping others."
Sir Miles Walker, from Hospice Isle of Man, said: "Robin had a quiet and shy way about him, and everyone enjoyed having him as one of the locals."
Funeral arrangements are expected to be announced later this week. A spokesman for Gibb told Reuters the funeral would be held in private and a memorial was being planned.
Gibb died at the London Clinic following a long fight with cancer. His second wife Dwina, sons Spencer and Robin-John and daughter Melissa were at his bedside.
Tributes continue to be paid to Bee Gees singer Robin Gibb following his death on Sunday at the age of 62.