The Government is to establish an independent statutory tribunal to deal with CervicalCheck claims.
The Cabinet has approved the appointment of Ms Justice Mary Irvine as Chairperson of the Tribunal.
Ms Justice Irvine's work will begin as soon as possible ahead of the establishment of the tribunal later in 2019.
The Minister for Health, Simon Harris, said he would also examine the early establishment of a non-statutory scheme to provide ex-gratia payments for the women affected by the non-disclosure of the audit.
The tribunal will be established based on the recommendations set out by Mr Justice Charles Meenan in his recent report on an alternative system for dealing with cases arising from CervicalCheck.
In a statement the Department of Health confirmed that hearings will be held in private and will be less adversarial than the current court process.
The tribunal will differ from the current court process in that it will be voluntary for all parties.
Minister Harris said that establishing a tribunal does not, in any way, restrict the right of women or their families to give evidence in public in the High Court, if that is their wish.