Northern Ireland will receive £150m from the United Kingdom government over the next two years to support the roll-out of ultra-fast broadband across the country.
Speaking outside Downing Street, Foster said the agreement would bring stability to the United Kingdom government as it embarked on the Brexit process.
There was similar anger in Wales, which also looks to the Barnett Formula for a share of any new public spending sanctioned by Whitehall.
"She said: "£1 billion extra pounds investment to keep Theresa May and her government in power is just a septic deal with a party that I abhor.
Foster, speaking to the Belfast Telegraph, said the deal would "support a minority government on a confidence and supply basis".
"An enhanced Northern Ireland voice articulating an agreed devolved government position could see more effective and inclusive representation of the unique circumstances of Northern Ireland at Westminster".
"If the election told us anything it is that the country is crying out for change".
Mr Green said the agreement should help to break the deadlock at Stormont which has meant there has been no power-sharing executive since elections in March.
Thewliss warned an alliance with the DUP could jeopardize the Good Friday Agreement on peace in Northern Ireland.
Northern Ireland will receive £1.5 billion in funding - consisting of £1 billion of new money and £500 million of previously announced funds - to be spent over the next two years on infrastructure, health and education.
Shrewsbury and Atcham MP Daniel Kawczynski said: "My attitude is we needed to secure an agreement with them to have a sensible, small majority to pass legislation through".
Political parties are still locked in negotiations to form a semi-autonomous power-sharing executive for the province almost four months after local elections there.
"However, while businesses will welcome the economic commitments laid out in this document, the number one priority for firms in Northern Ireland remains getting the Executive back up and running before the end of June".
A sitting of the assembly has been scheduled for Thursday at noon which could involve the election of a first minister and deputy first minister - but only in the event of a deal.
The agreement was signed by Tory chief whip Gavin Williamson and the DUP's Sir Jeffrey Donaldson while Mrs May and Mrs Foster, along with Damian Green and Nigel Dodds, watched on.