Plans for the eco-friendly property, which is to be built on Heber's Ghyll Drive, in Ilkley, near Bradford, had been refused and an appeal was lodged with the Planning Inspectorate.
The home, which is designed to look like large, irregular natural rock formations, will feature large, irregular-shaped windows, a courtyard and a natural outdoor pool.
Ilkley Town Council recommended refusing the planning application, which was lodged by businessman David Rasche, as it would be a "visual anomaly to the moorland".
They argued the land formed part of several areas of interest, including the South Pennine Moors Site of Special Scientific Interest and the South Pennine Moors Special Protection Area and Special Area of Conservation.
Ilkley Moor also forms part of the Bradford Pennine Gateway National Nature Reserve, backed by Natural England.
The council also noted the proposed development was close to the Swastika Stone, a prehistoric rock carving which is one of hundreds of Scheduled Ancient Monuments on Ilkley Moor.
But architects Shaw and Jagger said the property, which will be built on green belt land, takes "cues from the surrounding rocks and escarpments synonymous with the landscape."
They added: "The building depicts a series of monolithic elements embedded in the earth as the wild, dramatic environment looms around, attempting to overcome them."
The initial application was rejected by Bradford Council planners on 'non-determination', meaning a decision was not made within the required timeframe.
But the decision was appealed and the developers won a bid to the Planning Inspectorate in August through the country house clause.
The country house clause requires an isolated design of "exceptional quality" in that it "is truly outstanding", would "significantly enhance its immediate setting and be sensitive to the defining characteristics of the local area".
Nearby Ilkley Quarry is the site of the famous rock formation "Cow and Calf" which is named after its similarity to the animals.
The house has been named Fomorian - which refers to a supernatural race of giants in Irish mythology - and draws inspiration from one creature named Rombald who is said to have lived on the moor.
1. Shaw & Jagger Architects
Artist impression of the interior of the proposed Dwellinghouse, in Ilkley, near Bradford. Photo: SWNS
2. Shaw & Jagger Architects
Landscape near the proposed Dwellinghouse, in Ilkley, near Bradford. Photo: SWNS
3. Shaw & Jagger Architects
Landscape near the proposed Dwellinghouse, in Ilkley, near Bradford. Plans for a house designed to look like boulders on a famous Yorkshire moor have been approved following a planning battle to be built on green belt land. Photo: SWNS
4. Shaw & Jagger Architects
Artist impression of the interior of the proposed Dwellinghouse, in Ilkley, near Bradford. Photo: SWNS