Four men have been convicted for their roles in the gang-rape and murder of a young woman in a moving bus in Delhi last year.

Judge Yogesh Khanna delivered the verdict on Tuesday morning shortly after noon local time at the district court of Saket in south Delhi.

"I convict all of the accused. They have been found guilty of gang rape, unnatural offences, destruction of evidence … and for committing the murder of the helpless victim," Khanna said.

The bus cleaner Akshay Kumar Singh, gym instructor Vinay Sharma, fruit-seller Pawan Gupta and unemployed Mukesh Singh will be sentenced on Wednesday and are likely to face death by hanging, though life imprisonment is a possibility. Their lawyers said they would appeal.

With tears in her eyes and wearing a pink sari, the mother of the 23-year-old victim – who cannot be identified under Indian law – sat just a few feet from the four men who stood against a wall in the court as Khanna read the verdict.

Outside the courthouse, where dozens of protesters had gathered, a chant began quickly after the verdict: "Hang them! Hang them! Hang them!"

The trial of the men, aged between 19 and 34, started in January. One defendant, a bus driver, hanged himself in prison in March. The oldest of the six men accused of the attack on the physiotherapy student, he was alleged by police to have been the ringleader. The youngest among the alleged attackers, who was 17 at the time of the assault, was tried separately and was last month sentenced to three years in a juvenile reform home – the maximum possible punishment under Indian law.

The incident, which took place on a Sunday night in Delhi in December 2012, provoked outrage in India with protests across the country. It also led to an unprecedented national discussion about sexual violence and calls for widespread changes in cultural attitudes and policing, and legal reform. The international image of the country was damaged, with numbers of female tourists dropping significantly.

The victim's father, Badrinath Singh, told the Guardian he wanted the case to set an example to other women in India, where there has been a wave of sexual violence in recent years.

"I want other girls and women to know how brave my daughter was so her sacrifice does not go ashamed," Singh, 48, said shortly before the verdict.

Since the attack laws have been tightened and pledges made to improve the investigation and processing of sexual violence cases.

Vrinda Grover, a well-known activist, said the challenge was to make any changes "institutional".

"There is certainly much higher awareness now … but the Indian system has huge inertia," she said.

Much of the trial was held behind closed doors, with media excluded for many months. The men arrived at the courtroom on Tuesday morning wearing hoods to avoid photographers.

The mother of the victim, who suffered severe internal injuries when repeatedly violated with an iron bar, had called for all those guilty to be hanged, whatever their age.

"It has to be the death penalty," she told reporters earlier this week.

Singh, the victim's father, told the Guardian earlier this year that the family would push for a harsher sentence by any means possible in India and internationally.

All the men denied charges of rape, murder and destroying evidence. Two said they had been to listen to a music concert in a park on the night of the attack. One said he was driving the bus in which the assault took place and did not take therefore directly take part in the assault. A fourth, a 26-year-old drifter, said he had left Delhi for his village.

Police have said the juvenile convicted last month was the most violent of the attackers of the girl.

The prosecution case relied on testimony from 85 witnesses, a statement given by the victim before she died, DNA samples, dental records from bite marks on the victim's body that matched the teeth of some of the men and the evidence of her male friend, who was also badly beaten in the attack.

The victim's friend described how the couple were attacked after boarding the bus on the way home from an evening movie at an upscale shopping mall. The attackers beat the man and raped the woman, police and doctors told the court.

The victims were eventually dumped on a roadside layby on the outskirts of Delhi, and the woman died two weeks later in a Singapore hospital. Her ashes were later scattered in the Ganges river, near her ancestral village in rural India.

The men were also found guilty of robbing another man earlier in the evening of the incident.

Police described how the six had set out from the Singh brothers' home in a bus on a "joy ride". They then tricked the victim and her friend into boarding the bus and assaulted them shortly afterwards.

There has been widespread criticism of the fast-track court set up specifically to ensure rapid justice in the case, which is one of the most high-profile in India for many years.

The trial of the adult defendants started in January. The victim's father has said the idea of a fast-track court was a farce.

"This case should have wound up within a month after it started … We have waited so long. We don't want it to be for nothing," he said.

Gang-rapes, acid attacks and other acts of violence against women continue to be reported every day across India. In one recent incident a photojournalist was raped repeatedly by a group of men in a disused building in the commercial capital, Mumbai. The men have since been arrested. The victim of the attack was widely praised for her courage in complaining to police and identifying her attackers.

Rape victims in India often prefer to remain silent rather than risk social ostracism, and sexual harassment remains a daily reality for Indian women.

"Every day I take trains, buses and rickshaws and every day I get harassed one way or another. Last week it was a boy of only nine years old. We have to stand up to them. No one will take the first step unless you take it yourself," said Shurbhi Sharma, a 19-year-old student in Mumbai.

In the Delhi case, defence lawyers said police "tortured" and beat their clients into making confessions. Such abuse is systemic in India.

"He was crying. He said: 'Mum, mum, do something. Get me out of here. I never did anything wrong. I don't understand what is happening to me,'" Champa Sharma, mother of the defendant Vinay Sharma, said this weekend.

It is hoped fast-track courts such as the one where this trial was held will help improve a poor conviction rate. Many families of victims pressure their relatives who have been assaulted not to press charges, police often refuse to file cases for those who do, witnesses are systematically intimidated and courts rarely deliver swift justice in the few cases that are filed. Indian courts had a backlog of 33m cases as of 2011.