Wylfa on the Isle of Angelsey has been chosen as the first site, with a planning application scheduled to be submitted in two years' time.
Once work there has started, Horizon will then turn its attention to building a power station at Oldbury-on-Severn in Gloucestershire.
Both will have a capacity of up to 3,300mw and chief operating officer at Horizon Alan Raymant said they would have numerous advantages for the UK.
"New nuclear power would make a vital contribution to meeting the country's energy needs and tackling the challenge of climate change," he remarked.
According to the firm, nuclear power will play "a key part" in the challenge of supplying cheap electricity to the UK.
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