The property, on the grounds of the St Michael's College primary and secondary school, will now accommodate nearly two dozen third-level students.
Opposition had come from a group of parents of children at the school.
They are worried about the "potential for alcohol consumption within the school grounds".
A letter of objection to Dublin City Council outlined a series of concerns, including that the school will not be able to control the "noise levels" and "activities" of the students.
In a planning application, the religious order Congregation of the Holy Spirit, which runs the school, sought to change the use of St Michael's House to accommodate students, rather than priests.
The order is understood to be proposing a scheme to allow students studying at Pittsburgh's Duquesne University, which it founded in 1878, to undertake courses at UCD and Trinity College.
Despite the strong objections, An Bord Pleanala upheld the council decision. The board said the proposal would "not seriously injure" the residential amenities of surrounding homes.
But parents say their concerns remain. They believe the housing of students is "incompatible" with having a school on the land.