New Delhi court’s judge Satish Kumar issued the death warrant on Tuesday, ordering the four on death row to be executed on January 22 at 7am (01:30 GMT).
Indian media reports said Tihar prison in the capital, where the four are incarcerated, recently held a dummy execution to test the gallows.
The warrants were anticipated since the Supreme Court of India rejected one of the men’s final review pleas last month.
The convicts’ lawyers said they will file a fresh appeal against their execution. AP Singh, who represents convict Akshay Singh, said he will file a curative petition in the Supreme Court within a day or two.
Originally six people were charged with taking part in the brutal attack aboard a city bus, but one was released after a brief detention as a juvenile, while another committed suicide in prison while awaiting trial.
The condemned men still have one avenue of appeal remaining, and they can also petition India’s president for mercy.
The family of Jyoti Singh, the victim, said they were pleased with the ruling.
“This judgement will reinstate women’s faith in the judiciary,” Jyoti’s mother Asha Devi told journalists. “My daughter will finally get justice.”
Her father Badrinath Singh described it as a “good decision for the entire country”.
“But our struggle will continue for many other daughters who are in a similar situation across India,” he added.
Swati Maliwal, the chair of the Delhi Commission for Women, also applauded Tuesday’s court announcement on Twitter.
“I salute her mother who has fought for so long,” she tweeted. “It is a victory for all the fearless people of this country. This is the time to punish every rapist in the country so that a strong message is sent out.”
Jyoti Singh, 23, was attacked in December 2012 while returning home after visiting the cinema with a male friend.
Her assailants took turns to rape and violate her with a metal rod as the bus drove around the capital, before dumping her and her beaten-up friend in a roadside ditch.
Singh died of her injuries nearly two weeks after the attack in Singapore, where she had been flown for specialist treatment.
Tens of thousands of Indians took to the streets in protest, and the case led to a major overhaul of laws surrounding sexual assault.
It also spawned an award-winning documentary as well as a Netflix miniseries.
The scheduled executions came amid a revived debate over sexual violence in India after several headline-grabbing cases in recent months.
A woman in the northern state of Uttar Pradesh was doused with gasoline and set on fire by five men – including two who were out on bail after she had accused them of gang rape – on her way to attend a court hearing in her case. She died last month at a hospital in New Delhi.
In late November, the burned body of a 27-year-old veterinarian was found near the city of Hyderabad in southern India.
Police later fatally shot four men being held on suspicion of raping and killing the woman after investigators took them to the crime scene.
The police killings drew praise from people frustrated by the pace of the 2012 New Delhi case and condemnation from those who decried it as extrajudicial.