Speaking this evening to the BBC's "Reporting Scotland" programme, she said the Prime Minister had given her assurances there would be no effect on gay rights in the United Kingdom should a government be formed with the DUP.
The Conservatives and the Democratic Unionist Party are set to agree a written "programme for government", it has emerged, as the party's two most senior Westminster leaders flew to London to hammer out a deal.
The new deal gives Prime Minister Theresa May the required number of MPs needed to govern with a majority.
The Protestant unionist party also had links with outlawed paramilitary groups during the years of Northern Ireland's "Troubles".
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.
No 10 said the terms of the arrangement would be discussed at a Cabinet meeting on Monday.
In her statement Ms Hill said: "I have no doubt at all that Theresa May will continue to serve and work hard as Prime Minister and do it brilliantly". They quit Saturday after becoming a focus of blame for the Conservatives' election disaster.
Mrs May was working on a Cabinet reshuffle, although the election result makes it less likely she will risk alienating colleagues by making wholesale changes as she can not afford to have disgruntled former ministers sniping at her from the backbenches.
New iPhone update blocks drivers from texting behind the wheel
Passengers who are just riding, and not driving, will have the ability to disable the feature. Geskin also posted schematic images that purport to show the design of the new iPhone.
She also confirmed to German Chancellor Angela Merkel in a phone call yesterday that Britain was ready to begin Brexit negotiations "as planned in the next couple of weeks", reassuring European Union leaders who had expressed doubts after May's electoral losses.
"Gavin will have an important role to play in that".
A party spokesman confirmed the resignation of Hill, a combative character who one former colleague said had helped create a "toxic" atmosphere at the heart of the government. With the 10 DUP MP seats, the Conservatives will now have just enough votes to put them over the threshold.
The campaign failed to get "Theresa's positive plan for the future across" or "notice the surge in Labour support".
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.
Beleaguered British Prime Minister Theresa May is appointing new members of her government after several of them lost their seats in Parliament in this week's general election that proved disastrous for her Conservative Party. Her weakened position in the party rules out big changes, and May's office has said that the most senior Cabinet members - including Treasury chief Philip Hammond, Foreign Secretary Boris Johnson and Home Secretary Amber Rudd - will keep their jobs, but she is expected to shuffle the lower ranks of ministers.
Northern Ireland is the only part of the British Isles where same-sex marriage remains outlawed.
"From hubris to humiliation", said the left-leaning Guardian, while the Times headline read: "May stares into the abyss".