The deal, which also applies to the small number of multi-denominational and all-Irish schools, was worked out in talks conducted by an independent chairman, Dr Tom McCarthy from Trinity College, Dublin.
In future, boards will comprise two elected parents, two nominees of the school owners, the headteacher and an elected teacher. This "core board" will propose two other members from the wider community.
They will be appointed by the school owners who will also retain the right to appoint the chairperson.
The agreement provides a much-needed boost to the reform programme of the education minister, Niamh Bhreathnach, who hopes to incorporate it into a long-awaited Education Act next year.
The agreement is, however, not without its critics. The Irish National Teachers Organisation is unhappy with some of the provisions made for the minority Church of Ireland.
The two extra board members in its schools will have to be members of the Church of Ireland, and the church will be entitled to refuse admission to non-Church of Ireland pupils.
The Church of Ireland says these clauses in the agreement are essential if it is to retain the ethos of their schools, but the union believes that they are sectarian and possibly unconstitutional.