Guest, 57, who had been starring in the musical Wicked, was admitted to Melbourne's St Vincent's Hospital on Tuesday night, a spokeswoman for the production said.
He died peacefully in the hospital early this morning.
A hospital spokesperson told the Melbourne Herald Sun newspaper the family wanted the public to know he was surrounded by relatives and friends when he died.
Guest was born in Britain but enjoyed fame as a pop star in New Zealand in the 1970s and 1980s and spent a decade in Las Vegas.
His stage musical career took him to Australia where he starred in Les Miserables and The Phantom of the Opera.
He was awarded an OBE for his services to the New Zealand entertainment industry in 1994.
Guest was the world's longest serving Phantom having played the role a record 2289 performances over seven years in front of Australian and New Zealand audiences.
He had been at home with his partner Kellie Dickerson, Wicked's musical director, when he collapsed about 10pm on Tuesday, the Melbourne Age reported.
