A politician with celebrity status best known for his gaffes and rhetorical flourishes, Johnson will be appointed by Queen Elizabeth II at Buckingham Palace.
The 55-year-old will then deliver a speech outside his new Downing Street home, setting out the tone for his premiership.
The former foreign secretary became the new leader of the governing, centre-right Conservative Party on Tuesday.
Johnson's predecessor Theresa May was forced out after failing to get parliament to support a Brexit deal she struck with EU leaders.
Johnson has promised to overhaul the divorce deal, despite Brussels insisting no changes are possible.
He has tried to inject some vibrancy and optimism in the Brexit endgame.
But his promise of leaving the European Union, with or without a deal, puts him on a collision course with high-profile MPs in his own party who are utterly opposed to a no-deal Brexit, threatening his wafer-thin majority and raising the prospect of an early general election.
- Cabinet shake-up -
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Johnson has never hidden his ambition for power, using his trademark jokes and bluster to pull off unlikely electoral victories, but he takes over at a time of immense upheaval.
Besides Brexit, he will also have to handle the stand-off with Iran in the Gulf, after Tehran seized a UK-flagged tanker.
During his victory speech, Johnson urged Britain to "ping off the guy ropes of self-doubt and negativity" and pledged to unite a badly divided country.
After entering Downing Street, the former London mayor will start appointing his ministers.
"Boris will build a Cabinet showcasing all the talents within the party that truly reflect modern Britain," a source in Johnson's campaign team said.
Johnson will promote a record number of ethnic minority politicians to the Cabinet and increase the number of women around the table, the source said.
Former international development secretary Priti Patel -- a hardcore Brexiteer -- and Employment Minister Alok Sharma are in line for Cabinet seats, said the source.
Johnson beat Foreign Secretary Jeremy Hunt in the leadership contest by two to one in a ballot of party members, but Hunt is not certain to keep his Cabinet seat.
- 'Get Brexit done' -
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Three years after Johnson spearheaded the "Leave" vote in the 2016 referendum on Britain's EU membership, the UK remains a member after twice delaying its departure.
Johnson insists the latest deadline must be kept, calling it a "pivotal moment" in Britain's history.
"We're going to get Brexit done on October 31," he declared after winning 66 percent of almost 160,000 votes cast.
His government has a majority of just two -- 320 votes to 318 -- in parliament's lower House of Commons, meaning his administration will be precarious.
The main opposition Labour Party wants a general election and has pledged to force a vote of no confidence at a time of its choosing.
US President Donald Trump dubbed Johnson "Britain Trump" and suggested the new PM he would work together well with anti-EU figurehead Nigel Farage, whose Brexit Party has taken a big chunk of eurosceptic votes from the Conservatives.
Farage wrote in The Daily Telegraph newspaper that a swift general election was the "only way" for Johnson to get a meaningful Brexit through, for which he would "need the support" of the Brexit Party.
But Johnson-supporting Health Secretary Matt Hancock on Tuesday ruled out any form of electoral pact.
- 'Blast of optimism -
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London's stock market was slightly down Wednesday as Johnson prepared to take office.
All Britain's national newspapers featured Johnson on the front, largely saluting or with his thumbs up.
The Guardian said "Leave" leader Johnson was "largely responsible for the mess he now has to clear up", but "the signs are not promising".
The Sun said Johnson had the potential to be a "fantastic" PM but faced a "monumental" task, with an early general election looking "inevitable".
The tabloid called him an "inspiring blast of optimism after years of purgatory".
The Labour-supporting Daily Mirror said Johnson was a lying, incompetent, idle buffoon.
"Boris Johnson's clown act ceased to be funny years ago -- with people laughing at, not with, the conceited fool," it said.