Vinay Sharma, Pawan Gupta and Mukesh Singh had challenged the court’s 2017 ruling upholding their death penalty.
The brutal gang rape led to nationwide outrage and new anti-rape laws.
They have now exhausted all their legal options but can still file a mercy petition before India’s president.
The fourth man convicted in the case, Akshay Thakur, did not file an appeal but his lawyer says he plans to do so.
The victim’s mother told media that the Supreme Court ruling was “justice for all”.
“I have been struggling for six years, and today I am satisfied that justice has been delivered. The latest ruling has strengthened my belief in our justice system.”
She said it had been a difficult battle - but nothing compared to the 14 days she spent by her daughter’s side as she fought and lost the battle for her life, reports the BBC’s Divya Arya, who was at court.
The 23-year-old physiotherapy student was attacked on a bus as she and a male friend returned from watching a film in December 2012. Her friend was beaten up but survived.
She died of her injuries in hospital.
Six were arrested over the attack. 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.