ACT Attorney-General Simon Corbell has introduced legislation to erase the criminal convictions of men convicted of gay sex before it was legalised in 1976.
Mr Corbell said the bill was prepared in consultation with gay rights groups and would ensure those convicted would no longer be discriminated against when applying for work.
"The bill reflects the prevailing view of our community that consensual homosexual sex is not a criminal offence and that people should never have received a conviction for such an offence," he said.
"The potential negative impact of a criminal conviction is amplified when it is labelled a sex offence, a term that usually evokes images of non-consensual sexual exploitation."
Mr Corbell said the number of men with convictions was not known although it was estimated a small number of convictions did exist in the ACT.
A check of police records had revealed "a handful" of convictions, but records were difficult to access from before self-government and there could be more.
"The scheme created by the bill will allow people to apply to have their convictions erased permanently from their records," he said.
"This differs from the approach for spent convictions, where people's convictions still need to be declared when applying for working with vulnerable people checks.
"This approach acknowledges that consensual sexual activity should not be treated as criminal regardless of when it occurred."
Mr Corbell has previously said any process would need to be confidential and sensitive as many men were burdened with an unwarranted shame and stigma could exist many years after the conviction.
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.
"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."
NSW and Victoria moved last year to expunge criminal records for gay sex in 2014 with similar legislation already passed by 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 that 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's bill will be debated by territory politicians in coming months.
-With Kirsten Lawson