Downing Street said the arrangement will be put to the Cabinet for discussion on Monday.
Such an agreement would see the Northern Irish party's 10 MPs support the Conservatives on crucial votes when Parliament returns next week.
Number 10 said the arrangement will be put to the Cabinet for discussion on Monday.
A Downing Street spokesman added: "We welcome this commitment, which can provide the stability and certainty the whole country requires as we embark on Brexit and beyond."
Prime Minister Theresa May had sent Gavin Williamson, her chief whip, to Belfast to lead talks with the DUP.
A "confidence and supply" arrangement is a far looser deal than a formal coalition or pact.
It would mean the DUP backing the Government on its Budget and prevent it being brought down by motions of no confidence, but could potentially lead to other issues being decided on a vote-by-vote basis.
An online petition demanding a Tory-DUP minority government is stopped has amassed more than 580,000 signatures, amid concerns over its stance on gay rights, abortion and the death penalty.
Following the announcement, the Liberal Democrats called on Mrs May to make the terms of her deal with the DUP "clear to the British people immediately".
Lib Dem leader, Tim Farron said: "The actions of this Government will have profound implications for the Brexit negotiations and the future of our country.
At such a critical time, the Prime Minister must be clear with the people about the deal she has stitched up with the DUP behind closed doors."
Earlier today, several hundred protesters gathered in central London to voice their anger at Theresa May's attempt to form a government through an alliance with the DUP.