She also confirmed to German Chancellor Angela Merkel in a phone call yesterday that Britain was ready to begin Brexit negotiations "as planned in the next couple of weeks", reassuring EU leaders who had expressed doubts after May's electoral losses.
May's Conservatives lost their parliamentary majority in Thursday's vote and need the support of the 10 MPs from Northern Ireland's DUP to have a majority.
"We can confirm that the Democratic Unionist Party have agreed to the principles of an outline agreement to support the Conservative government," a spokesman for May said.
"We welcome this commitment, which can provide the stability and certainty the whole country requires as we embark on Brexit and beyond," he said.
The details of the agreement "will be put forward for discussion and agreement" at a cabinet meeting tomorrow, a day before the new parliament meets, the spokesman said.
There was no mention of what concessions the DUP may have asked for, amid growing concern about the influence of a party opposed to abortion and gay marriage, and which has proved hugely controversial in the past over the homophobic and sectarian views of some of its representatives.
The Conservative leader has been warned that her days are numbered after calling Thursday's vote three years early hoping to strengthen her hand going into Brexit negotiations with Brussels, only to lose her majority.
Senior party figures have cautioned against any immediate leadership challenge, saying it would cause only further disruption as Britain prepares to start the Brexit talks as early as June 19.
But media reports suggest they had demanded the departure of May's joint chiefs of staff, Nick Timothy and Fiona Hill, as the price for allowing the 60-year-old vicar's daughter to stay in office.
May put on a brave face after Thursday's vote, expressing sorrow for the MPs who lost their seats but refusing to acknowledge how her election gamble backfired.
"From hubris to humiliation," said the left-leaning Guardian, while the Times headline read: "May stares into the abyss".
The resignations of Timothy and Hill, on whom May had been heavily reliant since her previous job at the interior ministry, will be a personal blow.
Timothy said he took responsibility for the Conservative manifesto, including a plan for elderly social care that caused a backlash among core voters.
May is preparing to name the rest of her cabinet, after revealing Friday that her five most senior ministers would stay in their posts.
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