The former Mayor of London beat his rival Jeremy Hunt, taking 66 per cent of member's votes.
Of the approximately 160,000 Tory members across the country, 138,809 voted, with Mr Johnson taking 92,153 votes and Mr Hunt on 46,656.
Mrs May will formerly step aside tomorrow when she visits The Queen following her final Prime Minister's Questions.
The result could spark more Government resignations as ministers opposed to Mr Johnson's "do or die" pledge to pull the UK out of the EU on October 31, even if there is no Brexit deal in place, could quit before Mrs May's premiership officially ends.
Sir Alan Duncan quit as Foreign Office minister on Monday in protest at Mr Johnson's expected victory, predicting a "crisis of government" under his premiership.
Mr Hammond and Justice Secretary David Gauke have already given notice they will resign rather than serve under him.
Mr Gauke told The Times that newly elected Liberal Democrat leader Jo Swinson could take votes from the Tories in the event of a no-deal exit.
He said: "If we were to narrow our support to purely being those in favour of a no-deal Brexit I think we would be significantly out of touch with a lot of people who have traditionally voted Conservative - those who live in London, the home counties, and various other relatively affluent parts of the country."
However, Employment minister and Johnson-backer Alok Sharma called for Tory unity from ministers returning to the back benches.
He told BBC2's Newsnight: "I hope what they will do is reflect on the fact that the new Prime Minister, if it is Boris, will actually have a mandate from the parliamentary party and from the membership.
"What we will do if we have disunity in the party is risk a Corbyn government."
Mr Johnson will have to govern with a Tory-DUP majority of just two, after Dover MP Charlie Elphicke had the Conservative whip suspended after being charged with sexually assaulting two women.
The Government majority could be further reduced next week if the Tories lose the Brecon and Radnorshire by-election.