Only 36 out of more than 4,000 local responses supported it.
The county council planning committee approved the application by UK firm Third Energy to frack for shale gas at an existing drilling site near the village of Kirby Misperton, between Malton and Pickering.
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The fracking application is the first to be approved in the UK since 2011, when tests on the Fylde coast, in Lancashire, were found to have been the probable cause of minor earthquakes in the area, The Press Association reported.
Since then, two high-profile applications to frack in Lancashire have been rejected by councillors and are now the subject of appeals.
Planners had recommended the plan was approved, despite acknowledging that the majority of representations received in consultation were objections.
Vicky Perkin, a council planning officer, told the committee that, of 4,420 individual representations, 4,375 were objections and just 36 were in support of the application.
But the planning officers’ report said: “It should also be noted that there is national policy support for the development of a shale gas industry in this country and this is an important material consideration.”
The vote allows Third Energy to frack for shale gas using an existing two-mile deep well – called KM8 – drilled in 2013.
Seven of the 11 North Yorkshire County Councillors on the committee voted in favour of the application.
The result was met with boos and jeers from protesters who had gathered on the lawn outside County Hall, in Northallerton, during the two-day meeting.
Demonstrators shouted “shame on you” and “you will be held accountable”.
Speaking to the crowd, one protester said: “We remain opposed to fracking in Britain and across the world.
“We know fracking carries serious risks to local people, our health and water.”
She added: “This decision is not in our name.”
Committee chairman Peter Sowray told the meeting on Friday that this was “by far the most controversial application we have ever had to deal with”.
Dozens of speakers attended the meeting to outline their concerns over the hydraulic fracturing technique.
Objectors raised fears about the environment, safety issues, increased traffic, the effect on the landscape, health and the potential negative impact on tourism in the area.
But supporters addressed or dismissed the concerns, with experts, in areas including noise, water, ecology and landscape, making statements in support of the application.
Rasik Valand, chief executive of Third Energy, told the meeting: “If our application is successful, we will see it as a huge responsibility to deliver on our promises, not a victory. Promises to you, the local people.”
Lisa Nandy MP, Labour’s Shadow Energy & Climate Change Secretary, responding to the decision, said: “The controversy over this application shows fracking is still hugely contentious yet the Tories abandoned their promise of tougher safeguards.
“We need robust rules to offer communities reassurance that the environmental risks will be properly managed and local concerns will be listened to. There should be a moratorium until stronger protections are in place.”
Cllr Andrew Cooper, the Green Party’s energy spokesperson, said: “North Yorkshire County Council has let down the people of Kirby Misperton by passing this application for fracking today.
“The Green Party will continue to stand by local communities under threat from fracking operations and we will strongly oppose any attempts by central government to impose fracking against the will of local people.”
The Government has said it is going “all out for shale” to boost energy security and the economy.
But opponents fear fracking – in which liquid is pumped deep underground at high pressure to fracture rock and release gas – can cause problems including water contamination, earthquakes and noise and traffic pollution.
Environmentalists also warn that pursuing new sources of gas – a fossil fuel – is not compatible with efforts to tackle climate change.