The revised application from developer British Solar Renewables for the Wardon Hill scheme near Dorchester was given the green light by West District Dorset Council.
The development would be built on land used as a sports shooting ground.
The decision was made in line with planning officer recommendation, with the environmental benefits of the 10MW scheme judged to overrule any loss of sporting amenity.
An application made in 2014 was refused on grounds including its impact on the AONB and loss of the shooting ground, which has since closed.
Advisory body Sport England objected to the latest application, saying the shooting ground had been used by international squads for training.
"Should redevelopment be unavoidable, an equivalent (or better) replacement facility should be provided in a suitable location," insisted the body.
But planners said the ground had been closed for months and fewer objections had been received on a sporting basis than against the original application.
"It is considered that on balance the loss of the shooting ground is considered acceptable given the benefits identified," said the planning report.
It added that the environmental benefits of solar power, and the jobs the project would create, weighed in favour of the development.
Planners added that the development, including landscape mitigation proposals, would have an "acceptable" impact on the AONB.
Catherine Norris, principal planner at consultancy Alder King, said "significant effort" had been required to overcome the Sport England objections.
"Well-presented technical and merit arguments were key," she said. "This was a real team effort and we are delighted to have secured consent for this distinctive configuration on such an unusual site."
