A spokeswoman for Walsh – who is mentoring the groups in the 2009 series of the ITV1 show – confirmed on Sunday afternoon that he would not be appearing.
“He thanks you all for the messages of support at this sad time,” the spokeswoman said.
An X Factor spokeswoman confirmed to the BBC News website that the other judges, Simon Cowell, Dannii Minogue and Cheryl Cole would “continue with the show in the usual way”.
Gately, who was 33, was found dead on Saturday while he was on holiday in Majorca with his long-time partner Andy Cowles.
Earlier, Louis told the News Of The World that he was “devastated”.
“I’m in complete shock,” he said. “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.”
A post-mortem will be held on Tuesday after Spanish police were unable to determine the cause of death. However they have ruled out any suspicious circumstances.
A spokesman for Gately’s family said, “There’s no foul play involved and it’s not suicide.
“It’s just a tragic accident is what we’ve been told and we’re happy that that is correct information.
“There is nothing untoward, it’s not drugs, we don’t believe, it’s not suicide, it’s not murder, it’s not a fight. That’s what we’ve been told.
The remaining band members – Ronan Keating, Mikey Graham, Shane Lynch and Keith Duffy said that Gately had “lit up our lives”.
“We have shared such wonderful times together over the years and were all looking forward to sharing many more,” the band said in a statement.
“Stephen was a beautiful person in both body and spirit. Our love and sympathy go out to Andrew and Stephen’s family. We love you and will miss you forever.”
Others who paid tribute to Gately included Sir Elton John and his partner David Furnish, who originally introduced him to long-term partner Cowles.
“Stephen was the kindest, gentlest soul,” Sir Elton said. “We send our love and condolences to his partner Andy and to all his friends everywhere.”
Gately scored 16 top five hits as a member of Boyzone and also starred in a number of West End musicals. He also appeared on the 2007 series of Dancing On Ice, finishing in eighth place.