The four death row convicts are Mukesh, Vinay Sharma, Akshay Singh and Pawan Gupta.
"We will file curative petition in Supreme Court," said AP Singh, the convicts' lawyer.
The mother of the 23-year-old woman, who was gang raped and tortured on December 16, 2012, that led to her death, told reporters that the order (on death warrant) will restore faith of women in law.
ALSO READ: 'Mukesh Framed Because He is Poor', Alleges The Death Row Convict's Mother
Nirbhaya's father, Badrinath Singh, also expressed relief saying "It was a long journey, I am happy with the verdict," he said.
Welcoming the order, Delhi Commission for Women (DCW) chairperson Swati Maliwal said, "It's a victory for every citizen of the country, I salute the mother who kept fighting for the past seven years." .
"I would also like to thank the judges. Such rapists should be brought to justice in six months," she added.
The convicts were produced before the court through video conferencing.
The trial court had earlier directed Tihar jail authorities to seek within a week response from the four death row convicts as to whether they were filing mercy pleas against their executions with the President of India.
It was hearing the applications moved by Nirbhaya's parents and the prosecution (Delhi government) seeking issuance of death warrant against the convict.
The Supreme Court on December 18 had dismissed the plea of Akshay seeking review of its decision, saying review petition is not "re-hearing of appeal over and over again" and it had already considered the mitigating and aggravating circumstances while upholding the death penalty.
The 23-year-old paramedic student, referred to as Nirbhaya, was gang raped and brutally assaulted on the intervening night of December 16-17, 2012 inside a moving bus in south Delhi by six persons before being thrown out on the road.
She died on December 29, 2012 at Mount Elizabeth Hospital in Singapore.
On July 9 last year, the apex court had dismissed the review pleas filed by the other three convicts in the case, saying no grounds have been made out by them for review of the 2017 verdict.
One of the six accused in the case, Ram Singh, allegedly committed suicide in the Tihar Jail here.
A juvenile, who was among the accused, was convicted by a juvenile justice board and was released from a reformation home after serving a three-year term.
The top court in its 2017 verdict had upheld the capital punishment awarded to them by the Delhi High Court and the trial court.
(With additional information from Agencies)