The decision reverses a 2009 move by East Lothian Council to block the plan because of concerns over the environmental, health and transport effects.
Viridor appealed against the council decision, sparking an enquiry by a Scottish Government Reporter, who has now found in favour of the firm.
The decision has incensed protesters, who say the plant will be a blot on the landscape, will result in heavy emissions and will require waste to be transported for miles, increasing road traffic.
Philip Banks, chairman of the joint action group of community councils which opposed the plant, said: "We're obviously very disappointed.
"We think the arguments against the incinerator were overwhelming. The council rejected it unanimously and, for no new reason put forward, the Reporter has approved it.
"We think incineration is an old-fashioned technology, we think it is unsafe, we think it will have a detrimental effect on the area and it in no way meets the needs of the locality or the local council."
He said he was also disappointed in a system that allowed the Reporter to overturn the decision made by East Lothian's planning committee in November last year. The committee ruled against the proposal despite the advice of its own officers that it should be given the go-ahead.
Viridor said it was ready to push ahead with its plans to develop the firm's existing site in Oxwellmains, Dunbar, creating a plant which it says will generate enough power for 39,000 homes.
It says the plan will create 150 construction jobs and 47 skilled and professional posts, generating 10 million a year for the economy of East Lothian.
Viridor Scottish regional director Colin Paterson said: "The approval of plans for Scotland's most advanced energy-from-waste facility is good news for sustainability in Scotland and marks a key milestone on the road to delivering the Scottish Government's zero waste strategy.
"Zero waste won't happen without a network of new 'next generation' green infrastructure on the ground. Viridor is committed to supporting the public and private sectors and avoid costly landfill levies through recovering renewable energy from waste we can't recycle."