It was three years before the next scheduled election, and the conservatives already had a secure, if small, majority. However, Johnson said he backed May.
May called for a snap election in April, pledging to form a government that would guide the country through the Brexit process.
Earlier Saturday, May's top aides, her joint chiefs of staff both resigned.
The pound hit an eight-week low against the dollar and its lowest levels in seven months versus the euro before recovering slightly after May said she would form a government backed by her "friends" in the DUP.
The change was unlikely to significantly quell unrest within the party.
Reports had also been circulating that senior Conservative ministers in May's Cabinet had warned her that they would challenge her leadership of the party unless she became more inclusive, consulted more widely and fired Hill and Timothy. It aligns London more closely with the pro-British side in the divided province, where a power-sharing government with Irish nationalists is suspended.
May's office added that the Cabinet will discuss the agreement Monday.
The turmoil engulfing May has increased the chance that Britain will fall out of the European Union in 2019 without a deal.
She said: "They have achieved little propping up Tory governments in the past and put their own interests before those of the people". Now though, May's botched election leaves a question mark over her Brexit strategy.
"What that would allow the DUP is to say: we are not just acting in the interests of Northern Ireland".
One of the biggest political gambles in British history has apparently failed. And the Brexit talks are due to start in 10 days time.
Earlier, Downing Street issued a statement saying the DUP had agreed to the principles of a proposal to support the Conservatives. 'We need somebody who can talk and connect with people like Jeremy Corbyn does.
Some in Brussels may see this as an opportunity to drive a hard deal and dictate terms, Klass believes, while others may worry a weak prime minister won't be able to get parliamentary approval for a tough deal.
Opposition Leader Jeremy Corbyn said he thought there could be another election soon, after the vote on Thursday produced no clear victor and left Ms May under pressure from her own backbench and allies.
May continued to organize her government on Saturday. "I just don't see how she can continue in any long-term way".
Some Conservatives raised concerns about an alliance between the parties, with Scottish leader Ruth Davidson seeking assurances over LGBT rights from Mrs May.
This is in contrast to the coalition government formed between the Conservatives under David Cameron and the Liberal Democrats in 2010. "Theresa May has lost credibility and leverage in her party, her country and across Europe". But the election result meant it was unclear whether her plan to take Britain out of the bloc's single market and customs union could still be pursued.
The agreement emerged after Gavin Williamson, the Conservative Party's chief whip, spent the day in Belfast holding talks with DUP leader Arlene Foster and key DUP members.
While always striving for the "best deal" for Northern Ireland and its people, Foster said her party would always have the best interests of the United Kingdom at heart.
Johnson tweeted that an article in the Mail on Sunday newspaper headlined "Boris set to launch bid to be PM as May clings on" was "tripe". Yet, other than continuing vetoes over same-sex marriage and abortion legalisation, the DUP leadership will not be interested in reinforcing the party's religious outlook.
"I think its quite possible there'll be an election later this year or early next year, and that might be a good thing, because we can not go on with a period of great instability", he told the BBC's Andrew Marr on Sunday.