, he pointed out that the Tories’ 43 per cent vote share was almost unprecedented in recent decades.
And he added: “We have got to stop the narrative that Corbyn somehow won this thing.
“He barely did better than Gordon useless Brown when we beat him in 2010.”
Speaking after the leak, Mr Johnson told Sky News: "Theresa May got by far the biggest mandate anybody has got for my party for decades.
"She leads by far the biggest party in Government. Jeremy Corbyn did not win this election. It's absolutely right she should go ahead, form a Government and deliver on the priorities of the people.
"I'm going to be backing her and absolutely everybody I'm talking to is going to be backing her as well."
Mr Corbyn won more votes and seats than Mr Brown, but he trails the Tories by a greater margin than the ex-PM did.
The Foreign Secretary pleaded with colleagues to stop playing out internal fights in public.
He concluded: “The PM is a woman of extraordinary qualities and frankly the public are looking to us to get behind her with discipline and determination.
“On with the job!”
Boris Johnson has said he would be backing Theresa May Credit: PA:Press Association The Foreign Secretary threw his weight behind the beleaguered Theresa May Credit: EPA Michael Gove, Mr Johnson’s former ally turned bitter foe, responded with a message saying: “Boris is right.”
And backbencher Conor Burns added: "Spot on, Boris."
But one anonymous MP told BuzzFeed News that members of the WhatsApp group were "using [the PM] like a glove puppet" until Boris is strong enough to dethrone her.
Mr Johnson is currently considered the frontrunner if Mrs May does decide to step down or gets forced out in the wake of her election debacle.
His last bid to lead the party, after David Cameron resigned in the wake of the Brexit referendum, ended before it began as he failed to secure support from senior colleagues such as Mr Gove.
The message of unity suggests that he is keen not to make the same mistake this time around, with polls and bookmakers' odds indicating the leadership is his to lose if the PM goes.
Michael Gove is now apparently supporting Boris Johnson Credit: PA:Press Association And observers were quick to accuse Boris of deliberately leaking his WhatsApp post - Labour activist Mark Ferguson wrote on Twitter: "Want to see a WhatsApp message that was written to be leaked? Boris is on manoeuvres."
Mrs May has insisted she will not quit immediately despite losing her Commons majority, but says she will "reflect" on the dire result amidst calls from pro-EU backbenchers for her to step down within months.
She will face her MPs in the next two days, and could be told that she must resign, but it is considered more likely that she will be able to stay at least through the summer.
Along with Mr Johnson, the frontrunners to replace her include David Davis, Amber Rudd and Philip Hammond.
The Prime Minister is currently manoeuvring frantically to strike a deal with the Northern Irish DUP that would allow her to stay in power as head of a minority government.
'Calm down': Boris WhatsApp plea in full
Folks we need to calm down and get behind the Prime Minister.
1) She won more votes than anyone since Margaret Thatcher.
2) I can’t remember us having anything like 43 per cent of the vote.
3) We have got to stop the narrative that Corbyn somehow won this thing – he barely did better than Gordon useless Brown when we beat him in 2010.
4) We must get on and deliver for the people of this country – including a great Brexit deal.
5) We must not allow the media to spread mischief, not least because the public are fed up to the back teeth of politics and politicians and they certainly DO NOT want another election.
6) Yes of course we need to think about the lessons of this election but not in the papers.
7) The PM is a woman of extraordinary qualities and frankly the public are looking to us to get behind her with discipline and determination.
8) On with the job!