The local council plans to build a new denominational primary school in Bearsden.
It will replace the school which is currently located on the site, along with one in neighbouring Milngavie.
The Scottish government looked closely at the council's plans and is letting them go ahead with them.
Some parents at St Joseph's Primary in Milngavie and the Catholic Church had been fighting the scheme.
It would see St Joseph's Primary merged with St Andrew's Primary in neighbouring Bearsden.
The merged school would be sited in a new building on the current St Andrew's Primary School site.
Earlier this year the government "called in" the proposal to investigate it fully.
When the Scottish government calls in any proposal to close a school, it examines the process followed by the council and the information used to reach the decision.
But it cannot simply overturn a decision because it disagrees with it.
A spokesman for the Archdiocese of Glasgow said: "The Archdiocese strongly opposed the closure of St Joseph's Primary School and the ending of Catholic education in Milngavie.
"We share the dismay of parents, staff and pupils at this decision which will be a hammer blow for many in the affected community."
The chair of St Joseph's Parent Council Laureen McIntyre said: "The Scottish government's decision to give its consent to closure is very disappointing, but we have proven that St Joseph's primary school is a cherished part of our community and we will now consider our options, including a legal challenge."
The Catholic Church has said it is "dismayed" that plans to merge two primary schools in East Dunbartonshire are to go ahead.