In his column, Johnson firmly states four times that Britain will leave the EU on October 31 — the legal exit date after the UK's departure was twice delayed — in what will also be seen as an attempt to face down accusations he has been uncertain over the deadline.
He was criticised for appearing to soften his stance last week by saying an October Brexit was "eminently feasible", and has been under increasing pressure to commit to the exit date.
Sammy Wilson, the DUP's Brexit spokesman, yesterday signed up to a campaign by Tory MPs urging Johnson to guarantee to leave the EU by October 31.
He said: "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."
Johnson writes: "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."
Former Cabinet ministers Esther McVey and Owen Paterson have also joined the Stand up for Brexit pledge. McVey said: "We must accept that the deal is dead and prepare to leave the EU without one."
Boris eyes No10 as love nest
Boris Johnson is planning to move his girlfriend Carrie Symonds into Downing St with him should he win the Tory leadership contest, despite a row that led to police being called, the Daily Telegraph has been told.
Friends of Johnson are insisting nothing has changed in the couple's relationship after neighbours recorded them arguing loudly.
They said Johnson still plans to marry Symonds when his divorce to his second wife Marina Wheeler is finalised. Rumours had been circulating that Johnson and his partner had split and that their partnership was floundering even before the bust-up on Friday.
One source suggested Johnson was sleeping on the sofa and that explains why Symonds, a former Conservative Party director of communications, was so upset when wine was spilled on it. But yesterday, Johnson's camp was adamant the row was a typical contretemps.
A source said: "The couple intend to live together in No10 if he is elected Tory leader and to marry after his divorce is finalised."
If Johnson, 55, secures the leadership, and Symonds, 31, sticks with him, she would become the first girlfriend to move into Downing St as an official escort of an unmarried prime minister. The only time a prime minister has divorced and then remarried in office was the Duke of Grafton, in power from 1768 to 1770.
Johnson is finalising his divorce from Wheeler, a barrister, after they announced last September that they were separating.