Those judicial review proceedings have been discontinued by Mr Bain, Ms Adams said.
"This discontinuance does not resolve Mr Bain's underlying compensation claim, just the separate judicial review process. I plan to discuss next steps with my Cabinet colleagues over the coming weeks," she said.
"While the details of the agreement are confidential, I can confirm that there was no contribution made towards Mr Bain's compensation claim as part of this discontinuance."
Ms Adams said there would be a further announcement regarding the consideration of the application in due course.
Mr Bain spent 13 years behind bars for the murder of his family in 1995. He was later acquitted at a retrial.
A settlement conference as part of the now discontinued judicial review proceedings was held at the High Court at Auckland last month.
The meeting between Mr Bain's legal team, including Michael Reed QC and former All Black Joe Karam, and lawyers representing Justice Minister Amy Adams, was held ain chambers', meaning media could not report on proceedings.
Media were also barred from sitting in on the conference, held before Justice John Faire.
The compensation bid has hit a number of obstacles since Mr Bain first asked for redress from the Government in 2010.
An independent report into his case by retired Canadian judge Justice Ian Binnie ruled Mr Bain was innocent "on the balance of probabilities", and ordered him to be paid compensation for spending more than a decade in prison.
However, this was questioned by then Justice Minister Judith Collins. She ordered a review of the report by former High Court Judge Robert Fisher, who concluded it "would be unsafe to act upon the Binnie report".
In January 2013, Mr Bain filed for a judicial review of Ms Collins' decision.
Long-time Bain supporter Joe Karam said the judicial review was dropped after Ms Collins was replaced.
"The whole purpose of the judicial review was to stop Collins from carrying on with her secret process," he said today.
"When she was forced to come into the open in December 2012, it became very apparent that David Bain's compensation claim was effectively being scuttled by her. And when so when she effectively got the sack for other reasons, there wasn't much benefit in carrying on with the proceedings."
Ms Adams, through lawyers, indicated to Mr Bain's lawyers that she wanted to "move things forward", Mr Karam said.
"So, in a reasonably brief amount of time the thing has been settled and hopefully it'll be back on track in the proper way," he said.
"I'm sure the whole country is sick and tired of it; certainly David Bain is, and I absolutely am, as are David's lawyers. We now look forward to a responsible and expedient approach taken by the Government and we'll co-operate as best we can, as we did with Simon Power [Collins' predecessor]."
He hoped that the Minister and Cabinet would look at the case with some urgency, but didn't expect their decision in the next few months.
"It'll be quite a while I expect before we know where it's headed," said Mr Karam.
Mr Bain, who got married last year and became a father for the first time, also hoped it would be dealt with sooner than later, according to his closest ally.
"His life has been stuffed for more than 20 years now through various things that have gone wrong and certainly he would like it all over and done with and he can get on with his life with his new family," said Mr Karam.
Former Justice Minister Judith Collins declined comment, saying she was leaving all comment to Amy Adams.
Mr Bain was convicted and sentenced to life in prison in 1995 for murdering his parents, two sisters and brother at their Dunedin home, but was acquitted at retrial in 2009.
Last year he married Christchurch primary school teacher Liz Davies in a private ceremony. The couple welcomed their first child, a baby boy, at the beginning of December.
