A bench of Justices S Muralidhar and I S Mehta said the testimony of the victim and the DNA report, which was a clinching piece of evidence, have nailed the guilt of the convicts.
The bench, however, pulled up the investigating officer of the case for not conducting a proper investigation.
The high court, meanwhile, rejected the testimony of an eyewitness given in the trial court, claiming to have seen the accused persons committing the crime with the victim, saying he could not be accepted as a natural witness.
"In view of the victim's evidence, corroborated by the DNA report, this court is satisfied that the conclusion of the trial court on the guilt of the accused is correct. Accordingly, the appeals are dismissed," the bench said.
The trial court had on June 10, 2016 awarded life imprisonment till death to the five rapists, saying their "inhuman" and "brutal" acts of abduction and gangrape in 2014 had put a stigma on the reputation of the nation.
According to the police, the nine persons, all vagabonds, had robbed and gangraped the Danish tourist at knife-point on the night of January 14, 2014, after leading her to a secluded spot close to the Divisional Railway Officers' Club near the railway station.
The victim had come to the national capital on January 1, 2014, and stayed for a couple of days before leaving for Agra. After visiting several places, she returned to Delhi on January 13, 2014, and stayed in a hotel in Paharganj near the station. The next day when she was returning to her hotel, she lost her way and had asked one of the accused for directions when the men waylaid and gangraped her.