"Clearly this is an injustice that should have never been allowed to occur," Mr Corbell said. "The idea that you could face criminal charges and prosecution simply because you conducted yourself in a way that involved consensual homosexual acts is something that is abhorrent in today's society."

Mr Corbell was unable to say how many men had criminal records for gay sex. An investigation of police records had revealed just "a handful" of convictions for buggery and indecent assault, but records were difficult to access from before self-government and there could be more.

He would consult with lawyers and the gay community on how the scheme would work, but it probably would not involve the courts and would be confidential. People would apply to have their criminal record expunged.

"It needs to be confidential process because we're dealing with significant stigma and shame – unwarranted shame, of course, but nevertheless stigma that still can exist many years after the event so it needs to be confidential, it needs to be sensitive," he said.

Cases would be reviewed to ensure they involved consensual sex between adults.

"The issue of consent is a matter that will also need to be appropriately taken into account," he said. "Obviously we're dealing with consensual homosexual acts between adults and making sure that were able to confirm that the act involved was consensual is a important matter."

The deputy director of Australian Marriage Equality, Ivan Hinton-Teoh, whose group continues to campaign for same-sex marriage, said the move was much more than symbolic, with criminal convictions limiting people's ability to get jobs and having to be declared in many situations.

"This highlights the importance of removing prejudice and discrimination in our community regardless of when it occurred," he said. "We have ACT residents that have lived with the burden and the stigma of having a criminal conviction for a large part of their lives purely for the person that they loved."

The executive director of the AIDS Action Council in the ACT, Philippa Moss, also welcomed the move.

"Certainly we would be very pleased to see the ACT Government take this stand," she said. "It's ridiculous in this day and age to think that people would have a criminal record for homosexuality."

Confidentially was extremely important, especially given that many of the men would be older and some might have HIV, she said.

NSW and Victoria moved last year to expunge criminal records for gay sex, and Mr Corbell said he would be guided by those schemes and by a similar move in Britain. South Australia did the same in 2013, but its scheme involves application to a magistrate. In NSW, Victoria and Britain, the application is to a pubic servant – the secretary of the justice department in the case of NSW.

In NSW, the secretary reviews court and police records and must be satisfied the person who consented to the sex was 16, or 18 in the case of a teacher, step parent or health professional. Decisions can be appealed to a tribunal. If the convicted person has died, an application can be made by a family member, partner or lawyer.

Mr Corbell said legislation would introduced into the ACT Assembly later this year.

The move is another sign of the Barr Government's commitment to gay law reform.

On his elevation to the chief ministership in December, Mr Barr, the country's first openly gay leader of any state or territory, pledged to campaign for same-sex marriage in Australia, promising to be "a loud and passionate voice" to end discrimination against gay people.

"A number of people have observed, and I agree, that it is quite ironic that you can be elected chief minister, first minister of a jurisdiction, but you can't marry your partner of 15 years," he said.

"I want to assure gay and lesbian Canberrans, and indeed Australians, that I will continue to be a passionate voice for reform in this area."