So far, a total of eight candidates have announced they are standing for leader since Mrs May said she would resign on 7 June.
He took over as Foreign Secretary from Mr Johnson in 2018, and is seen as a steady if not outstanding Cabinet member.
Then, he faced allegations of betrayal after withdrawing support from Mr Johnson and running for leader himself, eventually helping to end both men's chances of becoming prime minister.
They joined Foreign Secretary Jeremy Hunt, International Development Secretary Rory Stewart, Health Secretary Matt Hancock and former Work and Pensions Secretary Esther McVey, in the battle for the leadership.
"But it's Boris who goes down well with voters and I want us to win the election - he's our best bet".
FILE - In this January 9, 2018 file photo, Matt Hancock smiles after leaving a Cabinet meeting in London.
"We can never take no-deal off the table but the best way of avoiding it is to make sure you have someone who is capable of negotiating a deal", the U.K.'s top diplomat said.
FILE - Demonstrators hold a banner during a Peoples Vote anti-Brexit march in London, March 23, 2019.
He added: "I know how painful it is to accept that your time is up and a new leader is required".
"I have done everything I can to convince MPs to back that deal, sadly I have not been able to do so, I tried three times".
He said: "She didn't start by levelling with people about the trade-offs".
Britain's fractious Conservatives are ruling as a minority government, and they rely on the support of a Northern Irish party to give them a working majority of just five in the House of Commons.More news: Britain set for new PM after May quits, as Brexit impasse remains
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Half of Brits believe the next Prime Minister should call an early election, polling has revealed.
Polls indicate that the Conservatives will be punished for their bickering over Brexit and could finish as low as fifth - their worst result in a national election.
Britain's main opposition Labour Party, which has also split over Brexit, is also likely to fare poorly, say pollsters.
But today the Prime Minister was very much a human, and whatever you think of her management - or mismanagement - of Brexit, no one can argue she's put on an unwavering performance.
The EU has extended the date until October 31 for Britain to reach an agreement on a withdrawal deal that will pave the way for its departure from the world's largest trading bloc.
Notoriously Johnson announced during the campaign: "My policy on cake is pro having it and pro eating it".
The pound and British stocks rose after news of May's resignation, as some investors appeared to hope it could unblock the political stalemate over Brexit, though analysts warn it could simply mean another delay to the European Union departure.
A party leadership campaign will officially begin after May quits, but already eight contenders have said they will run. May was broken by Brexit, serving one of the shortest terms of any recent British prime minister. Britain now faces an October 31 deadline to leave the EU.
Can new PM revive May's deal?
Tens of thousands of new members have signed up to join the Tories over the a year ago, dramatically increasing the electorate that will choose Theresa May's successor.
European Commission chief Jean-Claude Juncker says he considers May as "a woman of courage for whom he has great respect".
In an emotional address outside her Downing Street Office on Friday, May ended a dramatic three-year tenure of near-constant crisis over Brexit.
Spain said it now seemed nearly impossible to avoid a so-called hard Brexit, or clean break from the EU, and the bloc signalled there would be no change on the agreement despite European Commission President Jean-Claude Juncker learning of May's resignation "without personal joy".