Construction on the plant, which will be 70pc of the size of a true fusion reactor and be able to heat its hydrogen plasma fuel to 150m degrees Celsius, will begin next year and is expected to finish in 2025.
The Canadian company raised $100m (£71m) for its technology last year, but the plant is expected to cost a further $400m.
Its investors include Mr Bezos and Shopify founder Tobias Lütke. The start-up has secured support from the Government to fund the project, although the figure has not been disclosed.
The cost will be a fraction of the cost of ITER, a nuclear fusion megaproject being built in the south of France that is estimated to cost €22bn (£18.8bn).
ITER uses lasers and electromagnets that hold superheated plasma in a giant, doughnut-shaped container known as a tokamak, to produce fusion reactions. The total size of ITER's site is about 60 football fields.
General Fusion's technology takes a very different approach. Its spherical reactor compresses hydrogen in a ball of molten metal using 500 pistons that squeeze the core by firing up to 60 shots per minute. Heat from the reaction can be used to produce power.
Its reactor is only going to produce a fraction of the power planned by ITER - about 115 megawatts compared to 1,000 megawatts, but it is aimed at providing backup power generation and grid support to other renewable energy sources.
Amanda Solloway, the science minister, said: "This new plant by General Fusion is a huge boost for our plans to develop a fusion industry in the UK, and I'm thrilled that Culham will be home to such a cutting-edge and potentially transformative project."
Christofer Mowry, chief executive of General Fusion, said: "This is incredibly exciting news for not only General Fusion, but also the global effort to develop practical fusion energy."
- Telegraph Media Group