The Prime Minister, who has promised to quit the EU "do or die" by 31 October, said the UK was not "aiming" for a no-deal Brexit.
And he insisted talks between the two sides would be "at the races" if the controversial plan to avoid a hard Irish border could be scrapped.
The comments came as Mr Johnson prepared to head to Belfast for cross-party talks aimed at restoring power-sharing following the collapse of the Northern Ireland Executive more than two years ago.
His first visit to Northern Ireland as Prime Minister follows a deadlocked call with Irish Taoiseach Leo Varadkar on Tuesday, in which Mr Varadkar warned the Tory leader that the Irish backstop was "necessary" and cannot be scrapped in order to secure a Brexit deal.
"The Taoiseach emphasised to the Prime Minister that the backstop was necessary as a consequence of decisions taken in the UK and by the UK Government," the Irish government said in a statement.
"Noting that the Brexit negotiations take place between the UK and the EU, the Taoiseach explained that the EU was united in its view that the Withdrawal Agreement could not be reopened."
But Mr Johnson told the BBC that there was "no way" the arrangement - which would keep the UK closely aligned to EU customs rules if talks on the future relationship between the two sides fail - could stay in the withdrawal agreement.
"This is very much up to our friends and partners across the channel," he said.
"They know that three times the House of Commons has thrown out that backstop. There is no way that we can get it through.
"We have to have that backstop out of the deal. We cannot go on with the withdrawal agreement as it currently is, and everybody understands that. It's dead."
Mr Johnson added: "We need to get that message across to our friends. If they understand that then I think we are going to be at the races. If they can't compromise, if they really can't do it, then clearly we have to get ready for a no-deal exit. And I think we'll do it, I think that the people of this country are full of resolve and purpose."
TRANSITION PERIOD HINT
The Prime Minister's comments came as he hinted at extending the current one-year transition period contained in the withdrawal agreement in a bid to avoid the need for the backstop.
The transition period would see the UK temporarily stay in the customs union and single market in a bid to smooth the impact on business. In its current form it would run until December 2020.
But Mr Johnson suggested it could run for a "couple of years" as he insisted that the UK's no-deal Brexit preparations would not be a "wasted effort" even if Britain manages to leave the EU with a deal.
The Prime Minister said: "Some of the changes that are going to be necessary in the run-up to 31 October will be crucial anyway if we are going to come out of the customs union and single market, as we must, in the course of the next couple of years."
