Earlier on Saturday May lost her two closest aides as she struggled to reassert her leadership, having called an election three years early hoping to strengthen her hand going into Brexit negotiations - only to see the gamble backfire spectacularly.
Without a majority in the House of Commons, she could be forced to seek consensus on the approach she takes to Brexit, potentially by performing a U-turn on issues such as single market membership.
"We can confirm that the Democratic Unionist Party have agreed to the principles of an outline agreement to support the Conservative Government on a confidence and supply basis when Parliament returns next week", said a Number 10 spokesman.
Numerous key cabinet posts have already been declared as unchanged from the previous government, including Philip Hammond as Chancellor of the Exchequer, Amber Rudd as home secretary, Boris Johnson as foreign secretary, David Davis as Brexit secretary and Michael Fallon as the in-charge of the ministry of defence. She's then got to present a programme to Parliament.
Unionists appeared to have been sidelined when Sinn Fein pulled out of Northern Ireland's devolved assembly in January and surged at resulting regional elections, depriving Foster of her position as First Minister in the power-sharing government created by a 1998 peace deal.
However, senior DUP figures made clear they were looking at a limited "confidence and supply" arrangement - rather than a more formal coalition - leading to some MPs to predict that there could another general election before the year is out.
But the results left the Tories 12 short of the required number of Commons seat that will embolden anti-Brexit parties.
She insisted she would press ahead with Brexit talks, which are to begin in 10 days.
The party's manifesto architect, Ben Gummer, lost his seat to Labour.
Among Tory MPs there was anger at the way a 20-point lead in the opinion polls when she called the election in had been squandered in the course of a campaign which was widely condemned as flat-footed and uninspiring. And thanks to a strong showing in the election, the party has just enough seats to give May the majority she needs to govern. Northern Ireland is the only part of the United Kingdom where same-sex marriage is not legal, after the DUP exercised a veto.
We can accept the logic of support for Brexit providing the glue that would keep a deal together between the Conservatives and the DUP.
The talks with the DUP leader Arlene Foster will be on "how best they can provide support" for Mrs May's government.
The statement came as Mrs May's own MPs sharpened knives against her, and a jubilant Jeremy Corbyn demanded she make way for him to become PM.
In 2016, the party's leader Arlene Foster said about the pro-marriage equality movement: 'They are not going to influence me by sending me abuse - in fact, they are going to send me in the opposite direction and people need to reflect on that'.