Non-denominational school patron Educate Together will be involved in the running of secondary schools for the first time from next year.
Educate Together (ET) will be in charge of one in Blanchardstown West and will co-run another in Drogheda with the Vocational Education Committee (VEC).
"I am particularly pleased that Educate Together will be patron in one school and co-patron in a second school, given that ET was officially recognised by me as a second level patron just one year ago," Mr Quinn said.
The minister said his main concern when deciding the patronage of the new schools was parents’ demands for plurality and diversity in Irish schools.
"The successful patrons include those of a Catholic ethos, Church of Ireland ethos, multi-denominational and Gaelcholáistaí," he said.
ET was set up in 1975 and has until now only had patronage of primary schools.
Its schools are open to children regardless of their social, cultural or religious background.
ET campaigners in Dublin and Drogheda have welcomed the minister’s decision.
ET chief executive Paul Rowe said the new schools would nurture "critical and creative thinking and ethical citizenship".
Four of the new schools will open in September 2013 — all of which will be under VEC patronage.
The remaining 10 will open the following year — four will be under VEC patronage, one under the Le Cheile Schools Trust, two will be under the patronage of An Foras Pátrúnachta, one under the Church of Ireland.
The final two will be the ET and joint ET and VEC schools.
Meanwhile, the Irish Vocational Education Authority praised Mr Quinn’s commitment to the VEC sector — as eight of the 14 new schools would be under its patronage.
General secretary Michael Moriarty said the sector continued to expand and meet the needs of the growing population.
It said the fact that four VECs have been designated as patrons of five new schools to open in 2014 in Carrigaline, Co. Cork; Maynooth, Co. Kildare; Drogheda/Dundalk, Co. Louth; and Ashbourne, Co. Meath is a commitment to the future of VECs as they are reformed into Education and Training Boards (ETBs) in the months ahead.
Congratulating the VECs concerned, Mr Moriarty said: "The VEC sector needed a boost in this time of transformation and upheaval and this announcement is very welcome as it demonstrates the Minister’s on-going commitment to the VEC sector as they are re-structuring into ETBs."