Johnson, a former journalist, wrote a 4,000-word article in the Saturday edition of The Daily Telegraph newspaper to explain how Brexit can bring a "glorious" future to Britain and help it become "the greatest country on Earth."
He says Britain shouldn't seek to stay in the single market or the customs union, and should seize the opportunity to make its own way.
The timing of his Brexit broadside is important because May is scheduled to detail her own Brexit views at a much- touted speech in Italy on September 22.
Johnson was an avid campaigner for leaving the European Union in the 2016 referendum. He used the newspaper article to again raise the widely discredited idea that leaving the EU could allow Britain to add 350 million pounds (USD 475 million) a week to the National Health Service and argued that lifting regulations and reforming tax rules would allow Britain to prosper.
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Labour Party leader Jeremy Corbyn, whose party fared well in the general election vote, said through a spokesman that Johnson's Brexit views exposed the deep rifts within May's government.
"Boris Johnson has laid bare the conflicts at the heart of Theresa May's Government over Brexit and cut the ground from beneath the prime minister's authority," Corbyn's spokesman said.