Some senior Tories had made the removal of Hill and Timothy a condition for continuing to support May, who has vowed to remain prime minister.
May's Conservatives won 318 seats in the election, falling short of the 326 required for an absolute majority.
The party has since faced increased scrutiny over its anti-abortion and same-sex marriage stances, as well as members denying climate change is made-made.
The Protestant unionist party also had links with outlawed paramilitary groups during the years of Northern Ireland's "Troubles".
While not official party policy, DUP MP Sammy Wilson previously said the public had been "conned" into spending money to tackle the issue while serving as Northern Ireland environment minister. The DUP may provide the missing votes. Downing St. says the Cabinet will discuss the agreement Monday.
The decision to rule out a formal pact, which could make it more hard for the prime minister to govern, comes after her trusted joint chiefs of staff, Nick Timothy and Fiona Hill, resigned following May's failure to secure a majority in Thursday's general election.
The Conservatives lost their House of Commons majority in Thursday's election and will not be able to govern without support from the DUP's 10 members of parliament.
After frantic consultations with DUP leader Arlene Foster, the Prime Minister headed to Buckingham Palace to seek the formal permission of the Queen to form a new government, returning to No 10 to announce she had the "legitimacy" to continue in office.
"Gavin will have an important role to play in that".
The pair formed part of May's small inner circle and were blamed by many Conservatives for the party's lacklustre campaign and unpopular election platform.
The Conservative Party has been dependent on Irish politicians before: Prime Minister John Major relied on support from the Ulster Unionist Party to shore up his tiny majority in 1992-1997.
Theresa May is to head a minority Conservative government - propped up by the Democratic Unionists - after her General Election gamble backfired disastrously.
In a short statement outside Downing Street, which followed a 25-minute audience with The Queen, Mrs May said she meant to form a government which could "provide certainty and lead Britain forward at this critical time for our country".
If the Conservatives can secure 316 seats or more, the DUP's gains in Northern Ireland are enough to prop up May's government bid.
The Conservatives' losses on Thursday are likely to weaken May's hand in negotiating the U.K's exit from the European Union just before talks on the matter are set to begin later this month.