Under the agreement the 10 DUP MPs will vote with the Conservatives in the House of Commons to ensure the government can pass laws.
She said she would form a government with the Conservatives "our friends in the DUP" that would provide "certainty" for all of the United Kingdom and deliver Brexit.
"This gives me the confidence to believe that we will be able to work together in the interests of the whole United Kingdom".
May had been hoping to boost her mandate for Brexit negotiations which are due to begin in just 10 days' time, but hung parliament has left Tories weakened with less seats that fell below the 326 needed to form a majority government.
The Labour Party, led by Jeremy Corbyn, had been tipped to be decimated, but with a relatively high turnout at the polls boosted by younger voters, Labour made a significant recovery, picking up 31 seats to take 261 and well over 40% of the nationwide vote.
A brazen Theresa May spoke to reporters in Downing Street, accompanied by her husband Philip, as soon as her auto returned to Downing Street from Buckingham Palace shortly before 1.00 pm.
The DUP is concerned that any arrangement by which Northern Ireland could remain in the European Union, a key demand of the rival Sinn Fein Party, could potentially split Northern Ireland from the rest of Britain.
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They are now in the process of creating their first Climate Action Plan to develop strategies reach their emission goals. President Trump made a decision to pull the USA out of the agreement last Thursday.
"Theresa May has no intention of announcing her resignation later today", said Laura Kuenssberg, BBC political editor.
Prime Minister Theresa May will go to Buckingham Palace Friday to inform the Queen that she will attempt to form a government despite failing to win a majority in last night's general election.
Meanwhile, some senior conservative officials are even suggesting that May should consider resigning, and there are calls for Foreign Minister Boris Johnson to become the next prime minister.
It has also voted against introducing same-sex marriage and more liberal abortion laws to the province.
The ease of movement of goods and services from the Republic of Ireland into the North is going to be of the utmost importance to the DUP, which would necessitate remaining part of the customs union.
"I think that puts us in a fantastic position to deliver for Northern Ireland".
The UDA backed the DUP in this election by issuing a statement in support of the party's South Belfast candidate Emma Little Pengelly, "strongly urging" people to back her.
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