The Department of Education has chosen Educate Together to run seven of 12 new primary schools.
Two others will be Gaelscoils, while the remaining three will be led by local education and training boards.
The new schools, all to be established this year, will be located in Dublin, Kildare, Meath, Wicklow and Cork.
Education Minister Joe McHugh said he's pleased that parents in the areas involved will be offered a diversity of patronage.
He explained: "The establishment of these new schools forms an essential part of plans to ensure that sufficient new school places are available to cater for the growing cohort of pupils at primary level over the coming years.
"Parental preference has become a key determinant in deciding the patronage of new schools.
"I’m pleased to say that the views of parents as expressed through the process are strongly reflected in the decisions I have made on the patronage of these 12 new schools."
Paul Rowe, CEO of Educate Together, believes parents are looking for a different approach to education.
He observed: "They want their children best prepared for life in a diverse and globalised society.
"As a result of that, they are looking for an educational environment that is based on treating all children equally - irrespective of their religious, cultural or social backgrounds."
He added that all the successful patrons are delivering an alternative to the "monopoly of faith-based education" Ireland.
There are currently 84 Educate Together primary and 13 second-level schools in Ireland.