Past laws criminalising homosexual acts had not represented modern New Zealand for some time, she said.
"There is no doubt that homosexual New Zealanders who were convicted and branded as criminals for consensual activity suffered tremendous hurt and stigma, and we are sorry for what those men and their families have gone through and the continued effect the convictions have had on them."
Adams apologised on behalf of the Crown and said Parliament might consider a further apology when it passes the related legislation.
The law change will create a scheme uinder which people convicted of indecency between males, sodomy, or keeping places of resort for homosexual acts can apply to the Secretary of Justice for a pardon. Families of convicted people will also be able to apply on their behalf.
"Although we can never undo the impact on the lives of those affected, it's hoped that this scheme will provide a meaningful pathway for the convictions to be expunged," Adams said.
"This means people will be treated as if they had never been convicted and removes the stigma and prejudice which can arise from convictions for homosexual offences."
If an application is approved, the conviction will not turn up in criminal history checks and they can declare they have never had the conviction.
Asked why it took so long, Adams said she had originally been lobbied to make a blanket pardon and she was reluctant to do so. Officials needed to work out a scheme which did not remove liability for offences which were still considered criminal.
Adams said there was no precedent for the policy and the Government wanted to make sure it had properly considered any consitutional or other consequences.
The Ministry of Justice estimates around 879 people were convicted of homosexual acts before legalisation in 1986. Around 80 per cent are believed to have convictions which would still be offences under today's law, including under-age sex offences.
The step was applauded by politicians across the board.
Labour's Jacinda Ardern tweeted that she welcomed the news after sitting on the select committee which looked at the issue:
She later said the Government could have gone further by considering a blanket pardon or by dealing with some of the offences "in a more straightforward way". But she the policy was a "hugely positive move".
Labour MP Ian Lees-Galloway tweeted: "Good work Amy Adams. Strong leadership from the Minister of Justice."
United Future leader Peter Dunne described it as a "A good, sensible and compassionate decision" and Act leader David Seymour said it was "the right thing to do."
Act Party also tweeted: "Nice one @amyadamsMP. A win for freedom and equality."
The policy change in New Zealand comes after Britain agreed in October to pardon thousands of gay and bisexual men convicted under obsolete legislation.
It is known as the "Alan Turing law" after the World War II code-breaker who was posthumously pardoned in 2013 for his 1952 gross indecency conviction.
The policy change in New Zealand is in response to a petition by gay rights campaigner Wiremu Demchick, who requested a law change which set out a process for reversing convictions for consensual homosexual acts.
Demchick had hoped the Government would go further by carrying out a systematic review of all historic convictions.
The select committee which considered the petition heard from Kiwi men who said they were still haunted and traumatised by their convictions 30 years on.
Some of them said they had lost out on jobs or felt they were at a disadvantage when they went through background checks, or had abandoned careers because of their conviction.
