A 2012 report by former Canadian Supreme Court Justice Ian Binnie recommended compensation based on the view that Mr Bain was probably innocent - not innocent beyond reasonable doubt.
Mr Binnie's report noted that he was instructed that probable innocence was a minimum requirement for compensation.
Unhappy with the report, then-Justice Minister Judith Collins ordered a review of it by Robert Fisher QC, which found he made several errors of law.
"Mr Callinan is being asked the [question about innocence beyond reasonable doubt] at this stage because Cabinet has previously treated innocence beyond reasonable doubt as an example of 'extraordinary circumstances,'" Ms Adams said.
An "extraordinary circumstances discretion" allows Cabinet to consider compensation claims on a case-by-case basis and in the interests of justice.
Ms Adams said it would consider Mr Callinan's advice on the two questions on innocence before any further advice is sought.
"Mr Callinan is a distinguished and highly respected member of the Australian legal fraternity," Ms Adams said.
"He brings a diverse mix of experience and expertise, following an exemplary career of nearly forty years practice as a lawyer and nine years on the bench of the High Court of Australia."
The new inquiry was announced a month ago, with the Government agreeing to set aside all previous advice on the matter.
Ms Adams said that Cabinet did not have enough information to reach a decision on a potential payout for Mr Bain, who spent 13 years in prison before being found not guilty of murder in a retrial.
Mr Bain was imprisoned in 1995 after being convicted for killing five family members in Dunedin, but was freed after being found not guilty in a second trial in 2009.
Based on previous awards, Bain could be entitled to at least $2 million if Cabinet approves compensation.
Ms Adams selected Mr Callinan from a shortlist of retired judges with extensive criminal experience from both New Zealand and overseas jurisdictions.
"Mr Callinan's appointment is a significant step in progressing Mr Bain's claim for compensation and bringing some finality to the case," she said.
"I consider Mr Callinan to have the right breadth and depth of experience.
There is also merit in having an inquirer from outside New Zealand to remove any perception of influence of public opinion. Mr Callinan will bring a fresh perspective and dispassionate view to the inquiry."
The new inquiry will likely cost around $400,000. That would bring the total cost of the compensation case to nearly $1 million.
Ms Adams said work would start immediately and Mr Callinan expects to be able to report back to the Justice Minister within six months.
Hon Ian Callinan AC QC
• An Australian, Mr Callinan was appointed Queen's Counsel in 1978.
• Career has included high-profile criminal cases for both defence and prosecution.
• Retired from the High Court of Australia in 1998.
• Since retiring, completed work including a review of the Queensland Crime and Misconduct Commission.
• Appointed a Companion of the Order of Australia in 2003.
