Four men were convicted in September 2013 for murder, gang rape, theft, conspiracy and "unnatural acts" after a seven-month trial in a fast-track court.
A fifth man, the suspected ringleader, was found dead in jail in a suspected suicide, while the 17-year-old was sentenced to three years in a detention centre and has since been released.
Sentencing the four in 2013, Judge Yogesh Khanna said the case fell into the "rarest of rare category" which justifies capital punishment in India.
Media reports said a round of applause went up in court as the judgement was read out on Friday at the end of an appeal hearing that began last year.
Women's rights activist Ranjana Kumari called it a "historic judgement".
"This is a historic message to all the people, the criminal mindset who wrong women, who inflict violence on women, to know that if you do something like this you will be also paying for it by the severest punishment that exists in our laws of the land," she said on Indian news channel NDTV.