Adams confirmed an application process will come into play, with each case judged individually.
The passing of the Homosexual Law Reform Act in 1986 saw sex between males above 16 years old decriminalised.
However, convictions for consensual sex between men before the act remain in criminal history checks – and, in some instances, need to be disclosed during job applications.
“Although we can never fully undo the impact on the lives of those affected, this new scheme will provide a pathway for their convictions to be expunged,” said Adams.
“It means people will be treated as if they had never been convicted, and removes the ongoing stigma and prejudice that can arise from convictions for homosexual offences.”
Adams insisted the government will look to introduce legislation – and implement the scheme – this year. In excess of 1,000 people could be eligible to apply.