SYDNEY, Australia — Almost 30 years after an American mathematician’s body was found at the bottom of a Sydney cliff, a coroner has concluded that he was the victim of an anti-gay hate crime.

Since 1988, Scott Johnson’s family has lived with uncertainty over how the 27-year-old fell to his death off the North Head cliffs. On Thursday, Magistrate Michael Barnes, the state coroner, said he was “persuaded to the requisite standard Scott Johnson died as a result of a gay hate attack.”

The inquest was the third into Mr. Johnson’s death. The first, in 1989, ruled it a suicide. But years later, as evidence emerged that gangs had been attacking gay men in the cliffs around Sydney during the 1980s and ’90s, Mr. Johnson’s family began petitioning for a second inquest, which was held in 2012. It overturned the suicide ruling and recommended that the police reinvestigate.

Former Australian officials have said the police at that time were often hostile toward gay men and complacent about investigating their deaths. In 2013, the police of New South Wales, which includes Sydney, opened a review of 88 deaths of men between 1976 and 2000 to determine whether they should be reclassified as hate crimes.

No new arrests have been made since then, and Magistrate Barnes said there was insufficient evidence to determine who killed Mr. Johnson.

Mr. Johnson’s brother, Steve Johnson, an American tech entrepreneur who hired an investigator and pushed for the case to be reopened, said Thursday that he never believed his brother had committed suicide. When he learned about a 2005 inquest into three deaths from the same period, which found that the men had been driven off cliffs, “everything clicked into place,” said Mr. Johnson, 58, who was in court for the Thursday ruling.

On Thursday, Magistrate Barnes said the initial investigators in Scott Johnson’s case had “quickly jumped to conclusions without thoroughly and impartially examining all the facts.”

Magistrate Barnes said that the cliff from which Mr. Johnson fell was known to many as a so-called gay beat, a place where gay men would meet up. Former Australian officials now acknowledge that groups of teenagers and young men would target such areas with the intention of assaulting gay men, and that the police failed to see it at the time.

Mr. Johnson was pursuing a doctorate in mathematics at Australian National University when he died. He was in a relationship with an Australian man and had applied for permanent residency.

His brother described him as a gentle soul. “We climbed mountains together, we did mathematics together, we were fellow geeks together,” he said.

The ruling comes at a historic moment for gay people in Australia. Earlier this month, Australians voted decisively in favor of making same-sex marriage legal, in a nonbinding referendum. Legislation that would do so is making its way through Parliament this week.

The New South Wales police said in a statement Thursday that they had “conducted an exhaustive investigation over the past four years and presented all available evidence” about Mr. Johnson’s death to the coroner. They said the case remained open and that “any new information provided to police relating to the circumstances of Mr. Johnson’s death will be thoroughly investigated.”

A police spokeswoman declined to discuss the status of the review of 88 cases being re-examined as possible hate crimes.

Mr. Johnson said Thursday’s ruling brought him both relief and pain.

“It was anguishing losing Scott,” he said. “Now I know his final moments were filled with terror, and that’s just like living it all over again.”