Those judicial review proceedings had 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.
Long-time Bain supporter Joe Karam said he hoped the minister and the Cabinet would look at the case with some urgency, but did not expect a decision in the next few months.
"It'll be quite a while, I expect, before we know where it's headed," he said.
Ms Adams, through lawyers, indicated to Mr Bain's lawyers that she wanted to "move things forward", Mr Karam said.
Mr Bain, who married last year and became a father for the first time, also hoped the claim 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," Mr Karam said.
Mr Bain spent 13 years behind bars for the murder of his parents, two sisters and brother in 1995. He was acquitted at a retrial.
Mr Karam said the compensation claim had effectively been "scuttled" under former Justice Minister Judith Collins. He said the judicial review was dropped after Ms Collins was replaced.
