The Māori community leader Pauline Kingi will lead the inquiry into the appointment of police deputy commissioner Wally Haumaha.
The investigation is into the process that led to Mr Haumaha getting the job, in light of comments he made in 2004 in defence of three police officers accused of rape.
Internal Affairs Minister Tracey Martin said it would not look at whether Mr Haumaha was suitable for the role.
Pauline Kingi has been appointed as head of the inquiry.
Dr Kingi is a former senior public servant and community leader of 28 years, chairperson of Auckland University of Technology and Auckland regional director of Te Puni Kōkiri.
The terms of reference state Cabinet wants to determine if "all relevant information" was sought by the State Services Commission.
"And whether or not that information was provided to Ministers in order for them to make sound decisions and recommendations."
Acting Prime Minister Winston Peters said he did not know the exact cost of the inquiry but it could be in the ballpark of $150,000.
The inquiry will start on 6 August and run for a maximum of six weeks.