Mr Johnson achieved a landslide victory with 92,153 votes while Mr Hunt only got 46,656 votes.
The new leader will enter Number 10 after Theresa May takes her final Prime Minister's Questions in the Commons on Wednesday afternoon and then tenders her resignation to the Queen.
It comes after foreign office minister Sir Alan Duncan quit yesterday in protest of a possible Boris victory.
Chancellor Philip Hammond and Justice Secretary David Gauke said they also intended to quit if Mr Johnson was elected Tory leader.
Mr Gauke said he believed there were ‘parliamentary mechanisms’ that could prevent a no-deal Brexit which would ‘not necessarily’ involve bringing down a Johnson administration.
He stressed that he would not vote against a Tory government in a motion of no confidence if it was heading towards a no-deal Brexit.
The new prime minister 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.