The four remaining members of Boyzone described Gately as "our friend and brother".
"We have shared such wonderful times together over the years and were all looking forward to sharing many more," a statement said.
"Stephen was a beautiful person in both body and spirit. He lit up our lives and those of the many friends he had all over the world. Our love and sympathy go out to Andrew and Stephen's family. We love you and will miss you forever."
The Irish band had six UK number one hits in the 1990s and reformed in 2007.
Singer Ronan Keating is on his way back from the US and will join the rest of the group in Majorca.
Police said they were called to a house near Port d'Andratx on the western tip of the island on Saturday afternoon.
"At the moment it is not known how he died," the police spokesman said. "There are no signs of suspicious circumstances."
Louis Walsh's spokeswoman confirmed that the manager would not go ahead with his X Factor appearance.
Boyzone (with Gately on far left) reunited in 2007
His spokeswoman said: "He thanks you all for the messages of support at this sad time."
Walsh earlier told the News of the World newspaper: "We're all absolutely devastated.
"I'm in complete shock. I was only with him on Monday at an awards ceremony. We don't know much about what's happened yet.
"I only heard after The X Factor and we will rally around each other this week. He was a great man."
Bertie Ahern, former Irish Taoiseach, described Gately as a personal friend and his death as a "huge, huge tragedy" for Irish music and culture.
Singer Sir Elton John said: "David and I are stunned by this tragedy. Stephen was the kindest, gentlest soul.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.