A 2012 report by former Canadian Supreme Court Justice Ian Binnie said Mr Bain was probably innocent and should receive compensation.
But a peer review of his report by Robert Fisher QC, sought by then-minister Judith Collins, maintained Justice Binnie had made several errors of law.
Ms Adams said: "Given these events, it's my view that Cabinet doesn't have the information in front of it on which it could reasonably reach a decision."
"For that reason, the advice of both Justice Binnie and Dr Fisher will be set aside and I will appoint a new inquirer to conduct a fresh inquiry into Mr Bain's claim."
Based on previous awards, Bain could be entitled to at least $2 million if Cabinet approves compensation.
Ms Adams said it was important that the final decision on Mr Bain's case was "durable" and withstood the close scrutiny the case attracted.
"The New Zealand public rightly expects the Government to make a decision with the full set of facts and reliable advice in front of them.
"A fresh look will safeguard the integrity of the process and reassure the public that Cabinet will act on the best advice available.
"Despite the further delay, conducting a fresh inquiry is the best approach in the circumstances and enables Mr Bain's claim to be progressed on a proper and robust basis."
Ms Adams said the new inquiry would likely cost around $400,000.
That would bring the total cost of the compensation case to nearly $1 million.
In a statement, the minister said Mr Bain's claim for compensation fell outside existing Cabinet guidelines but ministers reserved a "residual discretion" to consider such claims "in extraordinary circumstances".
To satisfy the compensation threshold, Mr Bain would need to prove his innocence on the balance of probabilities and satisfy Cabinet that the circumstances were "sufficiently extraordinary" that it would be in the interests of justice for compensation to be paid.
Ms Adams said she had notified Mr Bain's representatives and she understood they were comfortable with the process.
"All parties have agreed to draw a line under what's happened and move forward in a constructive manner," she said.
A new inquirer to consider the case would be chosen soon.
A drawn-out battle
May 1995: David Bain convicted of killing five family members in Dunedin.
June 2009: Conviction quashed in a retrial after Privy Council appeal.
Nov 2011: Canadian judge Ian Binnie investigates compensation issue.
Aug 2012: Mr Binnie concludes Bain should be compensated. Justice Minister Judith Collins seeks a peer review from Robert Fisher QC.
Dec 2012: Fisher review says Justice Binnie's report was inaccurate and cannot be used.
July 2013: Bain's legal team seek judicial review of Ms Collins' handling of compensation claim.
Sep 2014: Amy Adams is made Justice Minister.
Jan 2015: Judicial review discontinued after confidential settlement between Govt and Mr Bain's team.
Feb 2015: Ms Adams confirms the compensation process will start afresh, with all previous advice put aside.
