The Prime Minister said he was “absolutely confident it will get over the line” in the next few weeks and that it would be “madness” not to go ahead with the project.
He said that if it were already operational this year, it would have cut fuel bills by £3 billion.
Labelling the problem as “myopia”, the outgoing Prime Minister said: “It is called short-termism. It is a chronic case of politicians not being able to see beyond the political cycle.”
He compared the UK to France and other countries: “Why have we never got back to that kind of rhythm?”
While not mentioning any previous Conservative leaders, Mr Johnson blamed the Labour Party for failing to develop nuclear while in office from 1997 to 2010. The Conservatives have been in Government, either in coalition or alone, since 2010.
“For 13 years the previous Labour Government did absolutely nothing to develop this country’s nuclear industry. They said it didn’t make economic sense,” he said.
“Thanks a bunch Tony. Thanks a bunch Gordon.”
Mr Johnson, who is due to stand down from office next week, said the new nuclear plant would create “tens of thousands of jobs”.
He said: “It will also power six million homes – that is roughly a fifth of all the homes in the UK – so it’ll help to fix the energy needs, not just of this generation but of the next.
“A baby born this year will be getting energy from Sizewell C long after she retires and this new reactor is just a part of our Great British nuclear campaign.”
Mr Johnson will be succeed in the role of Prime Minister by either Liz Truss or Rishi Sunak when the Conservative leadership election result is announced on September 5.
Addressing his successor, he urged them to “think about the future”.
“So no more national myopia, no more short-termism, let’s think about the future, let’s think about our kids and our grandchildren, about the next generation,” he said.
“And so I say to you, with the prophetic candour and clarity of one who is about to hand over the torch of office, I say go nuclear and go large and go with Sizewell C.”
The next Prime Minister will be forced to battle with a cost-of-living crisis, with some experts warning the fuel price cap could top £7,700 for a typical use household by April next year.
Taking questions from the media, Mr Johnson said it was “clear that come the new administration, there is going to be a further package” to help with bills, and suggested nuclear was one of the “medium and long-term” options to get bills down.
Asked what his future holds after leaving office, he said: “I think only time will tell is my answer on that one. But my intention and what I certainly will do is give my full and unqualified support to whoever takes over from me.
“Otherwise, really to get on with life.”
This is a breaking news story and will be updated