The European Commission said Britain agreed to modify significantly the terms of the project financing, reducing the burden on British taxpayers.
The scheme gives EDF a guaranteed power price of 92.50 pounds per megawatt-hour for 35 years, more than twice the current market rate.
The EU executive said the changes agreed by British authorities would cut the subsidy by more than 1 billion pounds and that Britain's share of any windfall profit will also be more than 1 billion pounds.
The project at Hinkley Point, southwest England, is part of Britain's strategy to replace a fifth of its ageing nuclear power and coal plants, and a major export contract for France.
Reuters reported earlier on Wednesday that the proposal had been approved.