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The young man, named by Australian media as James Teague, died in Dunedin Hospital about midnight, a hospital spokeswoman said.
The New South Wales man fell about 10m onto a concrete car park at The Glebe Apartments in the early hours of Thursday morning, Detective Matt Jones said.
He was flown by helicopter to Dunedin Hospital.
Mr Teague had been staying with friends at the hotel, and had been drinking alcohol before the incident.
The rugby fanatic was due to be watching the Waratahs take on the Brumbies in Sydney last night, the Sydney Morning Herald reported.
He had been with a group of friends who had been in New Zealand for at least a week, on a skiing and skydiving holiday in Queenstown.
Police said Mr Teague, from Paddington, had tried to climb from a second-floor balcony to the rooftop just before he fell.
Mr Teague's father, well-known eastern suburbs "society psychiatrist" Robert Hampshire, and his mother flew to his bedside, SMH reported.
Friends launched a social media campaign using the hashtag #clapforjames, asking the Waratahs to pay tribute to the fan before kick-off at Allianz Stadium, which resulted in a pre-game announcement.
"A big Tahs fan, 19-year-old James Teague had been looking forward to being here tonight," the announcement said.
"Tragically he was involved in an accident earlier this week and is now in a critical condition in hospital. Our thoughts are with the Teague family. We wish James all the very, very best for a full and speedy recovery."
A Waratahs spokeswoman said the club had been in touch with the family, who were grateful for the pre-game tribute to their son.
Best friend Gabby Richmond posted online that Mr Teague was "the sunshine in all of our lives".
"You brightened every person's day who you met," she said. "I will love you for the rest of my life . . . know how many lives you changed just by being you."
Another posted that Mr Teague was a "beautiful soul taken too soon".
Friend Matt Buxton posted that Mr Teague was a "rugby tragic and a great mate to many".
He attended the Scots College in Bellevue Hill and was studying at the University of Sydney.
In 2008, Invercargill electrician Shaun Hogan fell to his death at The Glebe after gaining access to the courtyard and climbing to the roof.
Queenstown construction worker Andy Pearson suffered chest and pelvic injuries after he slipped and fell from the third floor of The Glebe when it was being built in 2003.
Glebe Apartments manager Anne Henley said young people often would drink to excess in the holiday town.
"These kids have got to stop drinking and climbing."
She did not know what could be done about the problem.
"You can't ban drinking, I've got no answer -- maybe it's just the sheer number of people who are coming here now."
The group of friends Mr Teague was staying with were no longer at the complex.
- By Rebecca Quilliam of APNZ