As authorities braced for more unrest on the streets, police reinforcements could be seen fanning out across the centre of the Indian capital ahead of the return of the 23-year-old's body later in the day.
India's Prime Minister Manmohan Singh led the tributes to the victim but urged protesters to channel their anger constructively.
According to doctors in Singapore, the student lost her fight for life at 4:45 am (2045 GMT), nearly two weeks after the brutal attack that horrified India.
"She had suffered from severe organ failure following serious injuries to her body and brain," Kelvin Loh, the chief executive of Singapore's Mount Elizabeth Hospital, said in a statement.
"She was courageous in fighting for her life for so long against the odds but the trauma to her body was too severe for her to overcome."
After boarding a bus with tinted windows on December 16, the student was attacked by six drunk men who took it in turns to rape her and assaulted her with an iron bar before throwing her and her male companion off the moving vehicle.
She was airlifted to hospital in Singapore on Thursday -- a move that drew criticism from some Indian doctors who claimed it was aimed at removing her from the country as protests over the attack escalated.
Singh said he was deeply saddened by the death and that protests sparked by the case were "understandable".
"We have already seen the emotions and energies this incident has generated," he wrote on his website. "These are perfectly understandable reactions from a young India and an India that genuinely desires change."
Indian television news channels carried blanket coverage of the news, with the NDTV network running a ticker-tape headline "RIP India's Daughter".
India's High Commissioner to Singapore T.C.A. Raghavan told reporters that the woman's family was "shattered" by her death.
Her body was carried out of the hospital in a black bag by three workers, who placed it into a police van, after which it was driven to a morgue.
The body will be embalmed then released to her family in the afternoon, said workers at funeral parlour Hindu Casket. Raghavan said her body would be flown back to India later Saturday.
The decision to fly her out of India by air ambulance was taken at a meeting of Singh's cabinet on Wednesday and the government had promised to pay all her medical bills.
Home Minister Sushilkumar Shinde said the government's only concern was to ensure the victim received "the best treatment possible".
But Indian newspapers suggested the authorities, who have struggled to contain the nationwide protests over the attack, were keen to have her transferred out of the country.
An unnamed doctor who was part of a team of experts consulted about the transfer told The Hindu newspaper they had only been asked whether it was safe to move her and not whether it was the best course of action.
"The question was not whether there were any deficiencies in treatment that would be met by moving her... She was being given the best possible care," the doctor was quoted as saying.
Singh has ordered an official inquiry into the gang-rape and new laws to protect women as well as stiffer penalties for the worst sex crimes.
And he said Delhi police would soon launch a drive to recruit more female officers as a confidence-building measure.
The government has also announced plans to post the photos, names and addresses of convicted rapists on official websites to publicly shame them. The campaign will begin in Delhi, which has been dubbed India's "rape capital".
The Delhi gang-rape has shone the spotlight on a crime that occurs on a daily basis in India, with most such assaults taking place in rural areas.
Police said on Friday that a 15-year-old schoolgirl had had her throat slit after being gang-raped in the Pali Muqimpure area of Uttar Pradesh state. A hunt has been launched for three youths after the attack the previous day.