With the approval, which follows Planning Officer’s recommendation, the company will undertake hydraulically fracture at the KM8 well.
Third Energy CEO Rasik Valand said: "This approval, is not as a victory, but is a huge responsibility. We will have to deliver on our commitment, made to the committee and to the people of Ryedale, to undertake this operation safely and without impacting on the local environment.
The firm will initially determine the presence of gas in some samples in the hybrid sandstone shale formation. It will then determinate the ways the gas could be made to flow, process conditions and time period of the flow.
Upon assessing the flows, the company will test the flow performance for some months prior to making further decisions.
Commenting on the approval, UK Onshore Oil and Gas (UKOOG) CEO Ken Cronin said: "UKOOG welcomes the decision that has been taken today by North Yorkshire County Council, which helps to dispel many of the misleading claims that have been made about this application, as well as the process of hydraulic fracturing more generally.
"We look forward to Third Energy being able to conduct a test to see how much gas is under this area of North Yorkshire to power and heat homes and businesses."
British Chambers of Commerce acting director general Dr Adam Marshall said that fracking has potential to meet the country’s energy requirement and create new energy-related jobs in many areas.
The approval, however, has been opposed by campaign group Frack Off and environmental organization Friends of the Earth, among others, The Telegraph reported.
Friends of the Earth Yorkshire and Humber campaigner Simon Bowens said: "This is an absolute travesty of a decision but the battle is very far from over."