Incoming Justice Minister Andrew Little has confirmed he will order Teina Pora's $2.5 million compensation to be increased to match inflation.
The outgoing government had reserved the right to appeal against the inflation decision but Mr Little, who will be sworn in with the rest of the government today, confirmed to Morning Report that appeal would not go ahead.
"The High Court was pretty clear that when Cabinet considered it last time they hadn't considered adjusting by inflation as a matter of fairness. The High Court has now said that the government must do that, so we will do that."
Including time on remand, he spent nearly 22 years in prison for the murder and rape of Susan Burdett in 1992.
Mr Pora was convicted of her rape and murder in 1994 and was again found guilty at a retrial in 2000, but the convictions were overturned in 2015. In June last year, the government paid Teina Pora $2.5 million in compensation for the time spent in jail.
However, the compensation paid to him was based on 1998 guidelines that award $100,000 a year for loss of liberty.
Mr Little said during the election campaign Mr Pora's compensation should be increased and a Labour government would look at doing that.
He said he would also be obliged to look at previous advice to the government however.
"I'm told that there has been some advice that maybe has some contrary recommendations, and once I'm sworn in as minister I'll be obliged to look at that, but I'm equally obliged by the High Court ruling to now consider the issue of adjusting for compensation."
Labour has called for an independent review commission to be set up since 2013 over the Pora case, and others.
Mr Little told Morning Report he would be working on dealing with the process of resolving miscarriage of justice, also following the case of convicted double murderer David Tamihere.
"Like all these things where there are claims of miscarriage of justice - certainly where you've exhausted your appeal rights - at the moment we have this thing called the royal prerogative of mercy, it's a sort of legislative process, that's the process you would have to go through.
"I think the government has committed to dealing with miscarriages of justice including historical ones, and so the focus of my attention will be to get that stuff done."
Mr Pora's lawyer Jonathan Krebs said a report on the issue of increasing compensation said it would be unjust not to factor in inflation.
He said the legal team was "very very pleased" Mr Little had indicated the appeal will not go ahead, and the issue of inflation adjustment will be looked at.
Mr Krebs said he hoped the new cabinet would move quickly to remedy the situation.
Pike River talks 'as soon as possible'
Mr Little, who is also set to become the Minister Responsible for Pike River re-entry, said he hoped to speak with the families very soon.
"What I'd like to do as quickly as possible is get around the table with the families, their representatives and officials and go through, see what's on the table right now.
"I've seen some of the documentation and information that the families have got, I know some of the experts that they've retained and they are world class, so it's now just a question of seeing what the information is and putting a plan of action together."
He admitted it was possible there would be some information that the previous government had which could change the situation.
"Of course that's possible, I'll start getting briefings from departmental officials in the next couple of hours in fact - I think they start this afternoon.
"But I've seen the reports that the families have, these are reports by people that are world-renowned for mines recovery and mine recovery operations.
"It'll be interesting to see what the government previously has or hasn't disclosed but I think a commitment was made to those families that everything possible would be done to achieve recovery and that's what they want to see and that's what this project has got to be about."