In his first remarks as Prime Minister after being invited to form a government by the Queen, Mr Johnson struck an aggressively optimistic tone, saying: “The doubters, the doomsters, the gloomsters are going to get it wrong again."
With the Brexit deadline looming, the new Prime Minister said: “We aren't going to wait 99 days because the British people have had enough of waiting.”
Mr Johnson pledged to be a Prime Minister for the whole UK, stating: "It is time we unleashed the productive power, not just of London and the South East, but of every corner of England, Scotland, Wales and Northern Ireland - the awesome foursome that are incarnated in that red, white and blue flag."
He was cheered into Downing Street by supporters after meeting the Queen at Buckingham Palace.
They included Carrie Symonds, his girlfriend, who did not accompany him into Number 10.
Mr Johnson paid tribute to Theresa May’s “fortitude and patience” as well as her “deep sense of public service”, but hit out at “pessimists at home and abroad who think after three years of indecision that this country has become a prisoner to the old arguments of 2016 and in this home of democracy we are incapable of honouring a democratic mandate.
"And so I am standing before you today, to tell you the British people, that those critics are wrong - the doubters, the doomsters, the gloomsters are going to get it wrong again."
Mr Johnson added: "I will take personal responsibility for the change I want to see.
"Never mind the backstop, the buck stops here."
Mr Johnson said he was "convinced" a Brexit deal could be reached without checks at the Irish border and without the "anti-democratic backstop".
"It is of course vital at the same time that we prepare for the remote possibility that Brussels refuses any further to negotiate and we are forced to come out with no-deal.
"Not because we want that outcome, of course not, but because it is only common sense to prepare."
The Prime Minister said that he will succeed in delivering Brexit by the Halloween deadline "no ifs or buts".
"The people who bet against Britain are going to lose their shirts because we are going to restore trust in our democracy," he said.
"And we are going to fulfil the repeated promises of Parliament to the people and come out of the EU on October 31 no ifs or buts.
"I have every confidence that in 99 days time we will have cracked it.
"But you know what we aren't going to wait 99 days because the British people have had enough of waiting.
"The time has come to act, to take decisions to give strong leadership and to change this country for the better."
Mr Johnson said under "any circumstances" the UK would need to get ready to come out of the EU customs union and regulatory control.
"Fully determined at last to take advantage of Brexit, because that is the course on which this country is now set," he said.
"With high hearts and growing confidence we will now accelerate the work of getting ready.
"And the ports will be ready and the banks will be ready and the factories will be ready and business will be ready and the hospitals will be ready and our amazing food and farming sector will be ready and waiting to continue selling ever more, not just here but around the world.
"And don't forget that in the event of a no-deal outcome we will have that extra lubrication of the £39 billion and whatever deal we do we will prepare this autumn for an economic package to boost British business and to lengthen this country's lead as the number one destination in this continent for overseas investment."
Mr Johnson conceded to those who "prophesy disaster" that there will be challenges but he believes they can be mitigated.
"But if there is one thing that has really sapped the confidence of business over the past three years it's not the decisions we have taken, it's our refusal to take decisions.
"To those who say we cannot be ready I say do not underestimate this country."