The scheme, near the village of Wass, will provide a new home for a group of Benedictine nuns currently housed in Stanbrook Abbey, Worcester.
It is called a monastery, not a convent, because all Benedictine settlements are referred to as monasteries, whether they are for monks or nuns.
The project will provide the nuns with a 'peaceful landscape, a feature that is an important element within their contemplative life'.
The Bath and London-based practice's designs won a recommendation to approve from the North York Moors Planning Authority in June.
As this decision was a departure from the National Parks Policy on new developments, the Planning Authority was also required to notify the Secretary of State of its decision.
The scheme has now received full support from the government, thus enabling work to proceed.