Ms May said: "I hope the parties will look beyond their differences and come together with a shared sense of common objective to serve all communities in the best interests of Northern Ireland".
A Whitehall paper also revealed that new more flexible spending rules will be implemented to allow more scope over how devolved funding can be spent.
Ahead of the meeting at No10, Mrs Foster said she believed an agreement for the support of her 10 MPs is "close".
If the negotiations are concluded, Ms Foster and Mrs May are committed to making public the terms on which the ten DUP MPs will back the minority Conservative Party administration.
The deal comes after two weeks of talks between the parties since the election resulted in a hung Parliament.
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The DUP is Northern Ireland's largest party, and it has made clear it will only reach a deal with the Tories if tangible benefits are delivered - including jobs and investment in health, education and infrastructure.
May and Foster looked on Monday as the agreement was signed by the Conservative Party's chief whip Gavin Williamson and the DUP's Jeffrey Donaldson.
Speaking in Downing Street, Foster said government will channel an extra 1 billion pounds ($1.3 billion) to Northern Ireland over the next two years. May will also abandon Conservative pre-election plans to remove guarantees on the level of state pensions and cut winter-heating subsidies for retirees, she said.
Foster said the funding would "address the unique circumstances" of Northern Ireland.
And the SNP's leader in Westminster, Ian Blackford, said the deal showed Scotland is "seemingly to be offered little more than scraps from the table".
Other features of the agreement include a shared commitment to spend 2% of GDP on defence and guaranteed funding for agriculture in Northern Ireland after Brexit. And, will all parts of the United Kingdom receive the much-needed additional funding that Northern Ireland will get as part of the deal? The DUP has also agreed to back the government on any key votes in the House of Commons.
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Sinn Féin has opposed the extension of the covenant to Northern Ireland, given the British Army's role in the Troubles.
Later on Monday, May will publish details on how she intends to protect the rights of 3.2 million European Union nationals residing in Britain once the United Kingdom has left the bloc in 2019.
Tory grandee Lord Chris Patten told ITV's Peston on Sunday the alliance with the "toxic" DUP will be politically costly for the Conservatives. The current session is due to last for two years, meaning that the Tory-DUP deal is due to be formally reviewed in 2019.
"Where is the money for the Tory-DUP deal coming from?" the Labour leader asked.
"It's a very good deal for the DUP". "The Conservatives simply had no choice".
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