SYDNEY — Australian police arrested a man Tuesday in connection with the killing 32 years ago of an American university student whose death came to symbolize an indifference in Australian culture toward violence against gay people.

Scott Johnson, a 27-year-old PhD math student who had studied at the California Institute of Technology and Britain’s University of Cambridge, was thrown from a Sydney cliff, naked, in 1988 in an anti-gay hate crime, a coroner in New South Wales state ruled two years ago.

At the time of the initial investigation, police failed to take the case seriously and decided that Johnson had killed himself, even though he had shown no signs of depression, had not left a suicide note and his wallet was missing.

Johnson’s brother, Steve Johnson, began a three-decade campaign to persuade authorities to reopen the case.

Today, Sydney has a thriving and prominent gay community. Police officers march in the city’s annual Mardi Gras parade.

In the 1980s, however, packs of young men roamed popular meeting places for gay men, intending to beat and rob them. Gay men were told to carry whistles to call for help if they were attacked.

Victims were often too scared to complain to police. The officers sent to examine Johnson’s body did not have backgrounds in homicide investigations. They refused to believe that the top of the cliff above where Johnson was found, known for panoramic views of Sydney Harbor, could be a gay beat.

“It was pretty horrendous at that time,” said Nicolas Parkhill, chief executive of the state’s largest gay and lesbian health organization, ACON.

“You had the HIV epidemic and certain politicians were calling for gay men to be quarantined,” Parkhill said. “Australian culture was still very homophobic.”

Faced with pressure from the Johnson family and evidence that police had ignored endemic violence against Sydney’s gay community for years, in 2018 the New South Wales police force offered a reward of 1 million Australian dollars (about $650,000 at today’s exchange rates) for information about Johnson’s death.

Two months ago, Steve Johnson, a former vice president at Internet pioneer AOL, matched the offer.

On Tuesday, in the prosperous Sydney suburb of Lane Cove, police officers from a task force set up to investigate the killing arrested a 49-year-old man and later charged him with murder. He is expected to appear in court Wednesday. Police have not disclosed his name.

Steve Johnson told The Washington Post that last week the state’s head of police, Mick Fuller, personally called him to say the arrest was imminent. The police commissioner followed up once it was all over on Tuesday — a phone call Fuller later described as a “career highlight.”

The two men met for dinner in March of last year in Boston, where Steve Johnson, who had hired his own private detective, outlined leads in the case he believed the police had missed, according to a detailed account published by Business Insider.

On the day of the arrest, the Johnson family gathered for an impromptu celebration and champagne in Cambridge, Mass., although Steve Johnson’s oldest daughter, who was born a few months before her uncle died, had to join by Zoom because of covid-19 restrictions, he said.

“Everyone was crying,” Steve Johnson said in a telephone interview. “I don’t have any doubts in my mind that they have the right man.”

He said that he now hoped to learn about the details of his brother’s death. “Was it intentional?” he said. “Did they know each other beforehand, or was it a chance encounter?

“I was so close to my brother that being able to imagine or visualize what he went through has always been very important to me.”

Gay and lesbian advocates give the Johnson family credit for the shift in official attitudes, including a 2016 decision by the police to review the deaths of 88 men and transgender women killed between 1976 and 2000 — including Scott Johnson — to determine whether their deaths were hate crimes.

“They have kept the issue of hate crimes against the LGBTI community on the agenda this whole time,” said Nicole Asquith, a spokeswoman for the Australian Hate Crime Network.

“It’s an amazing moment to see one of those homicides come to the point where it can result in the arrest of an offender.”