The 'sampling' analysis is being conducted in the wake of the St Patrick's Guild revelations
An initial review of thousands of adoption records is due to be completed within four months.
Marion Reynolds - a former Deputy Director of Social Services in Northern Ireland - has been appointed as the independent reviewer, and will report to Children's Minister Katherine Zappone.
The terms of reference have been published on the Department of Children and Youth affairs website.
It comes after the child and family agency Tusla identified 126 cases where births were incorrectly registered by the former St Patrick's Guild adoption agency between 1946 and 1969.
They are cases where the adoptive parents of the child were recorded as the birth parents without an adoption order.
79 of the people affected may have no idea they were adopted and "may be entirely unaware of the true circumstances of their birth".
It has led to fears that there could be incorrect registrations from other adoption agencies - with Leo Varadkar having said the St Patrick's Guild discoveries may only be the 'tip of the iceberg'.
A 'targeted sampling' review will now be carried out of 150,000 records - dating back to the 1900s - from other adoption agencies, in a bid to discover if a larger trawl of the records is necessary.
Depending on the findings, the terms of reference say recommendations may include "more detailed analysis of records; an expansion of the number and types of records to be analysed; or such other steps as the independent reviewer considers appropriate in order to establish the potential to determine the extent of incorrect registrations".
While work is set to be completed within four months, Ms Reynolds will be able to produce an interim report "if she considers this appropriate at any stage".