In an interview with the BBC, the Conservative leadership frontrunner said he “did not believe for a moment” the UK would leave without a Brexit deal, although he was willing to do so if required.
Mr Johnson said the existing deal negotiated by Theresa May was “dead” and he could agree a new deal with the EU before the October 31 deadline because their was now a “different understanding” of what is needed in the UK and Europe.
"I think actually that politics has changed so much since 29 March,” he said.
"I think on both sides of the Channel there's a really different understanding of what is needed."
Mr Johnson said the UK would need the EU’s cooperation to avoid a hard Irish border or crippling tariffs on trade in the event of a no-deal Brexit.
He said there were "abundant, abundant technical fixes" that could be made to avoid border checks.
In response to why these do not exist yet, Mr Johnson said: "Well, they do actually, you have in very large measure they do, you have trusted trader schemes, all sorts of schemes that you could put into place."
He added there was "no single magic bullet" to solve the issue.
“It's not just up to us, it's up to the other side as well. And there is an element of course, a very important element of mutuality and co-operation in this,” he said.
“And we will be working with our friends and partners to make sure that we have an outcome that is manifestly in the interests of people, of businesses, communities on both sides of the channel.”
Mr Johnson also defended his record as foreign secretary and mayor of London, pledging to be a politician "who sticks by what (he) believes in".
Apologising for upset caused by gaffes during his tenure, he said he did not enjoy offending people but also claimed the public deserve a prime minister who speaks their mind.
The politician has previously come under fire for his handling of the continuing incarceration of British-Iranian citizen Nazanin Zaghari-Ratcliffe, and when he labelled Burka-wearing Muslim women "letterboxes".
He said in the interview: "What I pledge to, you know, and what I think the people of this country want to hear is, I will be a politician who sticks by what I believe in.
"Yes occasionally I may say things as I've said before, that cause offence, and I'm sorry for the offence and I'm sorry for the offence I caused, but I will continue to speak my mind because I think people deserve to hear what's going on in my head."
The current favourite to be the next Prime Minister also denied being careless with the truth when probed about his tenure as foreign secretary from 2016 to 2018.
Referring to Mrs Zaghari-Ratcliffe, Mr Johnson said: "I think of course people will want to point the finger of blame at me if they possibly can, but actually all that does is serve to exculpate, lift the blame of the people who are really responsible, who are the Iranian Revolutionary Guard.
"And if you look, talk about overachieving in the Foreign Office, we were told that we had to orchestrate, and we did, an international response to the poisonings by Russia in Salisbury, and we thought we would be lucky to get 30 Russian spies expelled around the world in support of the UK by other countries.
"We actually got 153 spies expelled around the world; I don't think there's ever been a diplomatic coup like."
"So don't look at what people say about me, look at what I actually deliver," he added.
Mr Johnson's interview came after police were reportedly called to the house he shares with his partner, Carrie Symonds, in Camberwell, South London.
He told the BBC he did not want to comment on reports, adding: "I do not talk about stuff involving my family, my loved ones.”
Asked for his response to being called a "coward" by his rival, Mr Johnson said: "Look you know I just always invoke the 11th commandment of Ronald Reagan which is 'thou shalt never speak ill of a fellow conservative'."
Mr Johnson has agreed to take part in an ITV event in two weeks' time, but Sky News has said it will have to cancel a similar event planned for Tuesday because he would not attend.