Mr Johnson, who leaves office on Tuesday, said he was confident that a funding deal for the plant would soon be finalised with the help of the taxpayer investment.
In a speech at the proposed site, already home to the decommissioned Sizewell A and operational Sizewell B, Mr Johnson condemned what he said were decades of underinvestment in the nuclear sector.
He said the "myopia and short-termism" of previous governments would be brought to an end under government plans to build eight new reactors at a pace of one a year.
The UK last opened a nuclear plant in 1995, although the Hinkley Point C project is well overdue and Sizewell C was given planning permission in July.
The new plant is expected to cost £14 billion ($16.2bn) and take almost a decade to build but Mr Johnson said a child born this year would enjoy its benefits into their retirement.
The reactor in Suffolk is expected to be built in partnership with French energy company EDF and could power the equivalent of about six million homes.
"We need to pull our national finger out and get on with Sizewell C," Mr Johnson said in what was expected to be his last major policy speech as prime minister.
"That’s why we’re putting £700m into the deal ... in the course of the next few weeks I am absolutely confident that it will get over the line.”
Mr Johnson said the government's push for energy independence after the invasion of Ukraine was already bearing fruit through more fossil fuel extraction from the North Sea.
Ministers will be given new powers to fast-track major infrastructure projects such as nuclear and offshore wind as part of the drive for domestic energy production.
"Nuclear always looks, when you begin, relatively expensive to build and to run," the prime minister said. "But look at what’s happening today, look at the results of Putin’s war. It is certainly cheap by comparison with hydrocarbons today.
However, investment in nuclear and offshore wind will not increase energy supplies this winter, when households are facing runaway bills for gas and electricity.
Environmentalists were unimpressed by his speech. Greenpeace scientist Dr Doug Parr said the £700m would be better spent on home insulation or cutting fuel bills than on nuclear reactors.
"The contrast between these lumbering white elephants and the dynamic, cost-cutting, innovative technologies in the renewables sector could barely be more striking," he said.
Mr Johnson declined to give any energy-saving advice to households for the winter but said there would be "more cash to come" from whoever wins the Conservative leadership contest.
Ministers have also expressed enthusiasm for a new generation of small reactors that could be used to power remote areas or hard-to-decarbonise industries.