Mr Johnson, an American mathematician who was based in Sydney, was discovered at the base of a cliff below a gay beat near Manly's North Head in December 1988.

His death was initially ruled to be a suicide, however then-coroner Michael Barnes in 2017 found the 27-year-old fell from the cliff "as a result of actual or threatened violence" by people who attacked him over his sexuality.

Police in 2018 announced a $1 million reward for information leading to the conviction of those responsible for his death.

His brother Steve Johnson on Monday joined police to announce he will match that reward by making a personal contribution of up to $1 million.

"With a reward of up to $2 million on the table, I am hoping that Scott will finally get justice," Mr Johnson said in a statement on Monday.

"Please, do it for Scott, do it for all gay men who were subject to hate crime, and now, do it for yourself."

Police Commissioner Mick Fuller said it was the first time such an offer had been made in NSW.

"It has been 31 long years in Scott's family's pursuit of answers, and the dedication to their brother is as inspiring as it is heartbreaking," Mr Fuller said in a statement.

"Steve has never wavered in his fight for justice; dedicating his time and efforts to Scott's honour, and today, he stands before you to offer his own money in hope that detectives get the elusive pieces to this puzzle."

Australian Associated Press