North Norfolk District Council's (NNDC) development committee voted in-line with planning officer Geoff Lyon's recommendation to approve British Solar Renewable's plans.
The solar farm is planned to be built at Egmere, four miles south of Wells.
It will consist of approximately 82,280 panels across 48 hectares on the former RAF North Creake airfield.
In a report to councillors Mr Lyon said: "The solar farm would generate enough electricity for the needs of approximately 4,326 homes annually.
"This would make it by far the largest renewable energy project in the district and would make a significant contribution towards meeting national renewable energy targets."
The solar farm is one of three major renewable energy projects planned for Egmere.
Plans for an anaerobic digester have already been approved and NNDC is carrying out a public consultation over plans to create a business park for companies working in the renewable energy industry.
Campaigners had expressed concerns about the size of the solar farm, the cumulative impact of it aligned to other developments and the impact it would have on the former North Creake airfield as an iportant heritage site.
At today's meeting, Nigel Morter, who lives at Bunkers Hill, the former control tower at the airfield, asked for certain conditions to be included in the proposals, including that an artifact search on the site is carried out by a competent person, that the view from the control tower to the runway was protected by slightly moving one of the boundaries and that information signs about the historical significance of the site were put in place.
Councillors agreed the application on provision Mr Morter's conditions were added.
Angus Macdonald, founder of British Solar Renewables, said they had worked hard to look at concerns regarding the visual impact of the development and as a result a landscaping scheme had been introduced as part of this.
Planning officers also gave an update on comments received from the Norfolk Coast Partnership and the Highways Authority stating they had no objections to the plans.