|Akshay Thakur, Vinay Sharma, Pawan Gupta and Mukesh|
Akshay Thakur, Vinay Sharma, Pawan Gupta and Mukesh were given the death penalty by a court in 2013.
Rejecting their appeal, Justice R Banumathi said the men committed "a barbaric crime" that had "shaken society's conscience".
The brutal gang rape led to nationwide outrage and and new anti-rape laws.
The 23-year-old physiotherapy student was attacked on a bus that she had boarded with her male friend as they returned home from watching a film in December 2012. Her friend was also beaten up.
Jyoti Singh - whose name was publicly revealed by her mother only in 2015 - died from injuries in a hospital 13 days later.
Media reports said relatives of Ms Singh applauded as the judgement was read out in court.
"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," Ranjana Kumari, a women's rights activist, told news channel NDTV.
Legal experts say it could still be months or even years before the sentences are carried out.
The four men still have the right to file a review petition in the Supreme Court. Their last hope lies with a plea for clemency to the president.
Six men were arrested over the attack on Ms Singh. One suspect, Ram Singh, was found dead in jail in March 2013, having apparently taken his own life.
Another, who was aged 17 at the time, was released in 2015 after serving three years in a reform facility - the maximum term possible for a juvenile in India.
Convicting the four men in 2013, Judge Yogesh Khanna said the case fell into the "rarest of rare category" which justifies capital punishment in India.
- 16 December 2012: A 23-year-old physiotherapy student is gang-raped by six men on a bus in Delhi, her male friend is beaten up and the pair are thrown out after the brutal assault
- 17 December: Key accused Ram Singh, the bus driver, is arrested. Over the next few days, his brother Mukesh Singh, gym instructor Vinay Sharma, fruit seller Pawan Gupta, a helper on the bus Akshay Thakur, and the 17-year-old juvenile, who cannot be named, are arrested.
- 29 December: The victim dies in hospital in Singapore from injuries sustained during the assault; body flown back to Delhi
- 11 March 2013: Ram Singh dies in Tihar jail; police say he hanged himself, but defence lawyers and his family allege he was murdered
- 31 August: The juvenile is found guilty and sentenced to three years in a reform facility
- 13 September: The four adult defendants are convicted and given the death penalty by the trial court
- 13 March 2014: The Delhi high court confirms the death sentence
- March - June: The convicts appeal in the Supreme Court and the death sentences are put on hold until the court takes a decision
Source: BBC News, May 5, 2017
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