Judge Yogesh Khanna said the case fell into the "rarest of rare category", which justified capital punishment.
"In these times when crimes against women are on the rise, court cannot turn a blind eye to this gruesome act," he said.
All the four suspects were teary eyed as they entered the cramped room dressed more smartly than on Tuesday when they were convicted of a string of charges including murder and gang rape.
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One of the men, Vinay Sharma, broke down in tears and cried loudly as the sentence was announced.
As the news broke, crowds inside the building and outside the courtroom roared with cheers and applauded the judgement.
The prosecution team congratulated each other, with lead lawyer Dayan Krishnan saying: "We did our job. We are happy with this sentence."
The father of the victim, who cannot be named for legal reasons, said the family was also satisfied as he left with his wife and sons.
"We are very happy. Justice has been delivered," he told reporters inside court flanked by his wife and sons.
