The glasshouse will be used for the organic production of plants, fruit and vegetables.
Herefordshire Council's conservation manager had expressed concerns about the scale of the glasshouse but felt a landscaping scheme produced addressed the visual impact of the scheme.
Little Dewchurch Parish Council recommended refusal due to the adverse impact on the Area of Outstanding Natural Beauty.
Sixteen letters of objection were received expressing concerns at increased noise and light pollution, increased traffic, excessive scale of the development and the fact there were more suitable sites in the holding for a development of this type and size.
As part of the conditions attached to the planning permission, two existing permissions for the erection of glasshouses elsewhere within the holding are to be rescinded.