The outcome of the ballot of about 160,000 Tory members was revealed just before midday at the QE2 Conference Centre in central London
Boris Johnson said it was an "extraordinary honour and privilege" to be elected Tory leader.
A Johnson premiership could spark more Government resignations after Sir Alan Duncan quit as Foreign Office minister on Monday in protest at his expected victory, predicting a "crisis of government" if Mr Johnson becomes PM.
Ministers opposed to his "do or die" pledge to pull the UK out of the EU on October 31, even if there is no deal in place, could leave before Mrs May formally gives up the premiership on Wednesday afternoon.
Chancellor Philip Hammond and Justice Secretary David Gauke have given notice that they will resign rather than serve under Mr Johnson.
Controversial, colourful and chaotic, Boris Johnson will be a prime minister unlike any other to enter Downing Street in recent times.
He believes he can give the UK back its "mojo" through an optimistic attitude and a "do or die" commitment to Brexit.
After a landslide victory in the Tory leadership contest, Mr Johnson is now on the threshold of Number 10 despite a string of gaffes and scandals that would have ended the careers of lesser politicians.
Instead the seemingly Teflon-coated Mr Johnson has been able to survive and prosper despite - or possibly due to - his capacity for attracting attention.
A row with girlfriend Carrie Symonds that saw police called to their home in the early stages of the leadership race was a glimpse into the complicated private life about which Mr Johnson tries desperately to avoid answering questions.
But it was his public actions - whether penning provocative columns or his record in the Foreign Office - which led to most scrutiny as Tory Party members decided on the next prime minister.
He has been repeatedly criticised for using racially charged or offensive language, including describing the Queen being greeted in Commonwealth countries by "flag-waving piccaninnies" and then-prime minister Tony Blair being met by "tribal warriors" with "watermelon smiles" while on a trip to the Congo.
In a 2018 Daily Telegraph column he described veiled Muslim women as "looking like letter boxes".
Mr Johnson said: "Insofar as my words have given offence over the last 20 or 30 years when I have been a journalist and people have taken those words out of my articles and escalated them, of course I am sorry for the offence they have caused."
He acknowledged that "occasionally some plaster comes off the ceiling as a result of a phrase I may have used" but insisted politicians should be able to speak frankly.
Mr Johnson has also faced repeated questions about his blunder as foreign secretary in the case of jailed British-Iranian Nazanin Zaghari-Ratcliffe, who he mistakenly said had been training journalists - comments which were seized on by the authorities in Tehran.
He has insisted that his comments made no difference - something disputed by Mrs Zaghari-Ratcliffe's husband, Richard Ratclffe - and said the blame for her continued incarceration should be on the Iranian regime rather than him.
His perceived lack of support for the UK's ambassador to the US, Sir Kim Darroch, over the leak of critical dispatches about President Donald Trump also concerned critics on the Tory benches and Whitehall.
Dealing with Iran and Mr Trump will be an early test for Mr Johnson, as he takes power at a time of heightened tensions in the Middle East.
Tehran has seized a British-flagged ship and Washington has urged the UK to join a US-led coalition to protect vessels in the Gulf - something that Theresa May's Government has resisted, favouring a European maritime force.
Although he has been all too willing to attract publicity for his political advantage, Mr Johnson, 55, has been reticent when it comes to details of his private life.
He met his first wife, Allegra Mostyn-Owen, while they were students at Oxford, and they wed in 1987, but the marriage was annulled in 1993.
His second marriage, to Marina Wheeler, ended last year after 25 years together, during which they had four children.
The marriage was turbulent - in 2004 he was sacked from the Tory frontbench over a reported affair with journalist Petronella Wyatt and the Appeal Court ruled in 2013 that the public had a right to know that he had fathered a daughter during an adulterous liaison while mayor of London in 2009.
Mr Johnson's latest relationship with 31-year-old Ms Symonds has been the subject of intense speculation about what her role will be in Downing Street.
Questions about his character were often raised during the leadership race, with a Tory member at a hustings event in Perth asking him whether a good prime minister needed to be "a loyal husband and father".
He was warned that his refusal to answer questions on the issue would mean that voters "come to their own conclusion and it may not be a favourable one".
Mr Johnson said: "Then I'm going to have to live with that."
Despite the reservations some Tory members have, Mr Johnson's status as a favourite of the Conservative grassroots was confirmed in the leadership election which saw him trounce rival Jeremy Hunt.
He also secured the votes of more than half of Tory MPs in order to make it through the parliamentary stage of the contest, including some pro-EU Conservatives who believe he can unite the party.
Mr Johnson's ability to reach out to voters who traditionally shun the Conservatives was demonstrated by his election as mayor of London in 2008 and retention of the powerful position four years later.
The Tory MP's decision to back Brexit in the referendum was a significant boost for the campaign, giving Vote Leave the high-profile frontman it needed.
After taking office as Prime Minister, Theresa May made him her foreign secretary - although he resigned in July 2018 over the direction she was taking on Brexit.
An old Etonian, Mr Johnson was a member of the notorious elite dining society the Bullingdon Club while at Oxford.
Although he has had his sights set on Number 10 throughout his political career, as a child he held even loftier ambitions.
According to his sister Rachel, the young Mr Johnson's goal was to be "world king".
For now, Downing Street will have to suffice.