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.
The spokesman indicated this would not be a formal coalition but a minority government with looser DUP support on a "confidence and supply basis".
The details of the agreement "will be put forward for discussion and agreement" at a cabinet meeting on Monday, a day before the new parliament meets, the spokesman said.
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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, only to lose her majority in parliament.
Senior party figures have cautioned against any immediate leadership challenge, saying it would cause only further disruption as Britain prepares to start Brexit negotiations as early as June 19.