The two parties had been locked in talks since the June 8 general election threw up a hung Parliament and May entered Downing Street on the assumption that the DUP's 10 MPs would be backing the Tories in Parliament to make up for a lack of overall majority in the House of Commons.
Under the so-called "confidence and supply" arrangement, the DUP will back May on key votes, which would threaten the government's survival if they were lost.
"We very much want to see that protected and enhanced and we also share the desire to ensure a strong government, able to put through its programme and provide for issues like the Brexit negotiations, but also national security issues," she said.
The talks between the two parties, which have been ongoing for weeks, focused on financial support for Northern Ireland and the shape of Brexit.
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The funds were expected to be used to boost Northern Ireland's economy and offer investment in new infrastructure, health and education.
DUP leader Arlene Foster said the "wide-ranging" agreement was "good for Northern Ireland and for the UK".
A three-page document outlining the terms of the agreement has been published today with further details on the financial arrangement expected later.
The DUP said the deal would apply for the lifetime of the Parliament, scheduled to last five years, but would also be reviewed at the end of the current session in two years time.
This means the DUP will support the Conservative government on votes on the Queen's Speech, the Budget, and legislation relating to Brexit and national security," a Downing Street statement said.
May shook hands with DUP leader Arlene Foster as she and other senior party figures arrived at Downing Street today to finalise the pact.
The two leaders then watched as Conservative party chief whip Gavin Williamson and his DUP counterpart Jeffrey Donaldson signed the historic documents for the confidence and supply arrangement.
She said the Tories had now recognised the case for higher funding in Northern Ireland and will publish details of financial support to be made available in due course.
Both parties had agreed there will be no change to the pensions triple lock and the universal nature of the winter fuel payment across the UK, things May had planned to change in her election manifesto but later dropped.
The Tories fell nine seats short of an overall majority after May's decision to call a snap election earlier this month backfired.
The support of the DUP will give the party an effective working majority of 13, as the other Northern Ireland party - Sinn Fein - do not take up their seven seats in Parliament and Speaker John Bercow and his three deputies - two of whom are Labour MPs - do not take part in votes.