He beat Jeremy Hunt on July 23, 2019 to conclude a process that lasted several weeks.
Boris Johnson does not believe for a moment the UK would leave without a deal, although he was willing to do so.
Asked about a row he had with his partner, he said it was "simply unfair" to involve "loved ones" in the debate.
The interview comes after Sky News said it would have to cancel a head-to-head debate on Tuesday between the two leadership contenders as Mr Johnson had so far declined to take part.
Work and Pensions Secretary Amber Rudd said she found Mr Johnson's decision to ignore live TV debates "very odd" and urged him to reconsider.
Mr Johnson has said the existing deal negotiated by Theresa May "is dead".
He insisted it was possible to broker a new deal with the European Union before the end of October because political landscape had changed in the UK and on the continent.
"I think actually that politics has changed so much since 29 March," he said referring to the original Brexit deadline.
"I think on both sides of the channel there is a really dierent understanding of what is needed," Mr Johnson also said.
At the moment, the UK is due to leave the EU on 31 October after the PM's Brexit deal was rejected three times by Parliament.
Mr Johnson said he would be able to persuade Brussels to resolve the Irish border issue - a key sticking point -despite repeated warnings from EU leaders that that was impossible.
He said there were "abundant technical xes" that could be made to avoid border checks.
When challenged that these do not exist yet, Mr Johnson replied: "Well they do actually; you have in large measure, all sorts of schemes that you could put into place".
But, he admitted, there was "no single magic bullet" to solve the issue .