The Middle Muir wind farm, proposed by developer Banks Renewables, would have a capacity of 60MW and include eight 136 metre-high wind turbines and seven of 152 metres.
The original application was for 17 turbines, but two were refused consent to mitigate landscape and visual impacts.
Scottish ministers accepted that there were landscape and visual impacts, but that Banks Renewables had taken steps to minimise them through the "siting, design and layout" of the development, according to the decision letter.
It added that ministers were of the opinion that the remaining impacts "are outweighed by the benefits of renewable energy generation the development will bring".
The two turbines dropped from the scheme were refused consent following objections from government advisor Historic Scotland.
The organisation had taken the position that the adverse impacts on Scheduled Monument Auchensaugh Hill cairn were not sufficient to warrant an objection but objected to turbines T14 and T16 because they would have a "significant impact on the cairn" and become "the single most dominant features" in certain views from the monument.