The Conservative leadership frontrunner – who has been under pressure to firmly commit to the deadline – said “we can, we must and we will” leave on the scheduled date.
Mr Johnson has previously insisted that Brexit will happen by Hallowe’en “deal or no deal” if he wins the race to succeed Theresa May.
But he appeared to soften his stance last week when he would only say that leaving the EU by that point was “eminently feasible”.
But, writing in the Telegraph, Mr Johnson said: “It is absolutely vital that we keep our eyes on the prize. It has been a long and parching march – but the oasis is finally in sight.
“We are just over four months away from the date on which, by law, we must leave the EU; and this time we are not going to bottle it. We are not going to fail. This time we are not going to shrink in fear from the exit, as we have on the last two occasions.”
And he added: “We must leave the EU on Oct 31 come what may. It will honour the referendum result, it will focus the minds of EU negotiators.”
However, he again failed to provide details on how he plans to renegotiate the Withdrawal Agreement or force through a no-deal Brexit against the wishes of MPs.
The former Foreign Secretary – who is also facing intense scrutiny of his private life following a noisy row at the flat he shares with his partner in the early hours of Friday morning – said the country was “positively aching” for Brexit exactly three years on from the referendum.
And he vowed to “turbocharge” the UK economy if he wins the top job, repeating a pledge to boost Britain’s broadband access and promising “higher wages and higher productivity all round”.
‘THE DEAL IS DEAD’
The renewed vow to quit the European Union on 31 October came as Tory Brexiteers stepped up their campaign to ensure whoever wins the leadership commits to that exit date.
Former leadership contender Esther McVey joined fellow Conservative MPs Priti Patel, Iain Duncan Smith and Owen Paterson in signing a new “stand up for Brexit” pledge.
The Tatton MP said: “We must accept that the deal is dead and prepare to leave the EU without it.”
But Mr Johnson’s leadership rival Jeremy Hunt urged the ex-mayor of London to “man up” and face public scrutiny on a string of policy pledges.
Writing in The Times, Mr Hunt said he was “not interested in debating Boris’s private life”.
“But I do want to quiz him on how he can ‘guarantee’ we will leave the EU on October 31 if parliament votes to stop a no-deal Brexit, as it did in March,” he added.
“I want to know what he really means by ‘reviewing’ HS2 or his ‘grave reservations’ about the third runway – surely he has had long enough to decide what he thinks?