Gately, 33, died in his sleep yesterday following a night out on the island, according to the News of the World.
Bandmate Shane Lynch said that he, Ronan Keating, Mikey Graham and Keith Duffy will fly out to Majorca today following the news.
The group's manager Louis Walsh is quoted as saying: "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."
Meanwhile, a friend of Keating told the newspaper that the singer is "completely distraught", saying: "No-one saw this coming. He loved Stephen like a brother, they were so close, it's absolutely floored him.
"It's a massive shock to everyone and no-one can take it in yet. He was a man in the prime of his life, and this is a huge tragedy."
Irish-born Gately, who announced that he was gay in 1999, leaves behind husband Andrew Cowles. The pair married in a civil ceremony in London in 2006.
Boyzone split in 2000 and Gately went on to have a Top 10 solo album and three Top 20 singles before being dropped by his record label. He also played the lead in the West End production of Joseph and the Amazing Technicolor Dreamcoat and later appeared on ITV's Dancing On Ice.
The boyband reformed in 2007 and released two singles and 'best of' album Back Again... No Matter What last year. They have recorded a new album for release in spring 2010.