In an interview with the Sunday Telegraph, the Prime Minister said this pledge means that voters can be "100%" certain that a Conservative government will "unblock" Parliament and deliver Brexit.
Last month, Mr Johnson's Withdrawal Agreement Bill was approved in principle at its first hurdle when MPs voted 329 to 299 for it, but the blow came when they rejected the hasty timetable by 322 to 308.
It effectively put paid to his promise - "no ifs, no buts" - to take the UK out of the EU by October 31.
Mr Johnson told the newspaper: "All 635 Conservative candidates standing at this election - every single one of them - has pledged to me that if elected they will vote in Parliament to pass my Brexit deal so we can end the uncertainty and finally leave the EU.
"I am offering a pact with the people: if you vote Conservative you can be 100% sure a majority Conservative government will unblock Parliament and get Brexit done."
The Prime Minister has also moved to firm up his party's immigration plans, after he appeared to row back from the promise of cutting immigration "overall" during the week.
On Thursday, Mr Johnson said the Conservatives' promised points-based immigration system "may" mean the numbers come down "in some sectors", after Home Secretary Priti Patel had earlier said a Tory government would "reduce immigration overall".
Now the party is pledging to get "overall migration down", and under a range of measures, the "vast majority" of migrants will need a job offer to come to the UK to work, regardless of where they are from in the world.
Meanwhile, a Savanta ComRes poll for the Sunday Telegraph, based on a survey of 2,052 British adults online from November 13-14, has the Conservatives on 41%, Labour on 33%, the
Lib Dems on 14% and the Brexit Party on 5%.
A YouGov survey for The Sunday Times puts the Tories on 45%, Labour on 28%, the Lib Dems on 15% and the Brexit Party on 4%.
The poll results came as Jeremy Corbyn said he had secured the "unanimous agreement" of senior Labour figures regarding the details of his party's manifesto.
The document - expected to be launched on Thursday - was being billed as "more radical" than the manifesto campaigned on in the 2017 election.
Tensions were expected at the clause V meeting, particularly over immigration, but party chairman Ian Lavery told Sky News that discussions were "very amicable" with "very little disagreement at all".
However, the Mail on Sunday said it was told that the free movement issue was "fudged", with the newspaper reporting that the plan is to state in the manifesto that freedom of movement for EU citizens would continue if the UK stayed in the bloc but is a "matter for the negotiations".
The Sunday Times reported that the party had scrapped a plan to maintain and extend freedom of movement, while the Mail on Sunday also reported that the manifesto is set to include a ban on working for more than 48 hours a week, a widespread nationalisation programme, the abolition of academies and free schools, an expansion of the sugar levy, and a new cabinet minister for women.
The Labour Party would not comment on reports about the contents of the manifesto.