In the judgment convicting the accused, the judge had noted that there was strong evidence that they had committed the brutal gang rape and a "cold-blooded murder".
During arguments on the point of sentence on Wednesday, special public prosecutor Dayan Krishnan had demanded the noose for all convicts for the "grotesque and diabolic" crime.
"There is no chance such criminals can be reformed. If death is not given to such criminals, the common man will lose faith in the courts. Society feels no woman is safe. It is for the courts to change that perception by handing down harsh punishment," he said.
Lawyers for the four convicts had pleaded for mercy, saying they were young, didn't have previous criminal records and should be given a chance to reform.
The incident on the night of December 16, 2012 had sparked spontaneous public outrage across India, bringing thousands of people out on the streets in protest against authorities' failure to ensure women's safety.
It triggered uproar in Parliament and prompted the government to enact a tough law to deal with crimes against women, increase policing and fast-track rape cases across the country.