The deal comes after two weeks of talks between the parties since the election resulted in a hung Parliament.
The DUP's 10 MPs will back the Tories in key Commons votes, starting with the Queen's Speech later this week, but there will be no formal coalition.
The talks focused on financial support for Northern Ireland and Brexit.
The DUP has claimed the UK government has agreed to improve the treatment of military veterans in Northern Ireland as part of the agreement but played down reports that it had sought £2bn in extra funding for Northern Ireland in return for their support.
Mrs May shook hands with DUP leader Arlene Foster as she and other senior party figures arrived at Downing Street on Monday to finalise the pact.
Under the so-called "confidence and supply" arrangement, the DUP will line up behind the government in key votes, such as on the Queen's Speech and Budgets, which would threaten the government's survival if they were lost.
On other legislation, however, the DUP's support is not necessarily guaranteed - although the Northern Ireland party is expected to back the majority of the government's programme for the next two years after many of its more controversial policies were dropped.
Theresa May fell nine seats short of an overall majority after the snap election, meaning she is reliant on other parties to pass legislation, including relating to the terms of the UK's withdrawal from the EU.
The support of the DUP will give her an effective working majority of 13, given that Sinn Fein do not take up their seven seats and Speaker John Bercow and his three deputies - two of whom are Labour MPs - do not take part in votes.
Several senior Tories had advised her to govern without any formal agreement with the DUP, arguing the unionist party would not be prepared to bring Mrs May down and run the risk of triggering a fresh election given their longstanding hostility to Jeremy Corbyn and other senior Labour figures.
Former PM Sir John Major warned that a formal association with the DUP could undermine attempts to restore power-sharing government in Northern Ireland while some MPs said the DUP's socially conservative stance on issues such as gay marriage and abortion could damage the party in the longer term.
Labour have demanded details of how much the deal will cost UK taxpayers and what financial promises have been made.
But the Tories and DUP have said the pact will give the UK much-needed stability as it embarks on the Brexit process.