The Church directly controls about 3,000 of the country's 3,300 primary schools. At present it appoints half the board members and the chairpersons.
In future each board is likely to comprise two Church nominees, two elected parents, one elected teacher, the school head and two others from the "wider community".
These two additional members will be expected to uphold the ethos of the school, which will be further safeguarded in the deeds of trust.
The outline of the deal was arrived at on the eve of publication of a long-awaited government White Paper which sets the framework for a major shake-up of the entire education system in the republic.
Among the many decisions are: statutory provision for parents' associations in all schools and for parental representation on boards of management; the raising of the school-leaving age from 15 to 16; the creation of 10 regional education boards; seven-year terms for all new school heads; a gender balance on all school and college boards.
Reaction has been generally positive to the document except for one section which deals with the length of the school year. It provides for statutory obligations on all boards to ensure that schools are teaching pupils for a prescribed minimum number of hours and days per year - this reflects official concern that there are too many early closures and half days.
It also proposes that pupils not involved in state exams in the summer should no longer take holidays early - instead they should remain in school and take house exams and assessments while their teachers who are usually on holiday, should go on in-service training or staff development programmes.
The employers' organisation has welcomed this section as the Irish secondary school year tends to be shorter than in other countries.
Predictably, however, the proposal has not found favour with the teacher unions or with many pupils.