The council had rejected the applications at Pond Farm and Selbrigg Farm, but these decisions were overturned by an inspector after an inquiry.
The local authority will now ask the High Court to quash the inspector’s decision to allow the turbines, which would be 78m high at Selbrigg and 66m at Pond Farm.
Council leader Tom FitzPatrick said: ‘We are very much in agreement with the vast majority of the local community on this matter. The proposed wind turbines would detract from the unique landscape of this beautiful area and destroy its tranquility.
‘We have discussed our options and carefully considered the next step, which is to apply to the High Court to quash the inspector’s decision.’
An earlier application by Pond Farm’s promoter Genatec for a 86.5m-tall turbine was rejected by the council in 2012, approved by an inspector on appeal and then overturned by the High Court in February 2014.
A joint statement by the turbine promoters given to the Eastern Daily Press said: ‘We will have to wait to hear what the council’s reasons are before we can respond properly, but are disappointed to learn that yet more taxpayers’ money will be spent challenging a decision that the secretary of state is in favour of, and many local people support, that would generate not only green electricity but also business rates for the district, while other public services are being threatened with cuts.’