The pair have been in the firing line after the PM's gamble of calling a snap election backfired, with disgruntled Conservatives highly critical of the role of Mr Timothy and Ms Hill played in the campaign.
Ex-minister Gavin Barwell, who lost his seat in Thursday's election, was last night named as the new chief of staff.
In a resignation letter published by ConservativeHome yesterday, Nick Timothy took the blame for his party's disastrous manifesto policy to raid the estates of pensioners after they die to pay for their social care.
In particular, he said he regretted the decision not to include in the Tory manifesto that these payments would be capped.
'But I would like to make clear that the freakish media reports about my own role in the policy's inclusion are wrong: it had been the subject of many months of work within Whitehall, and it was not my personal pet project'.
Another Conservative MP, Anna Soubry, told the BBC after the results came in that May has to "obviously consider her position" and take personal responsibility for the "dreadful" election campaign and "deeply flawed" manifesto.
Ms Hill said it had been a pleasure to serve in government and she believed Mrs May would continue as prime minister.
Theresa May's closest advisers created a "toxic" environment in Downing Street and put forward "batshit crazy" ideas, according to a former aide of the Prime Minister.
But he slammed May's style of governance as tone deaf to her own Cabinet ministers and MPs, whom he said were better in touch with voters on the ground.
In his statement, Mr Timothy said: 'The reason for the disappointing result was not the absence of support for Theresa May and the Conservatives but an unexpected surge in support for Labour.
"The Prime Minister has tonight spoken with the DUP to discuss finalizing a confidence and supply deal when Parliament returns next week", the statement said.
Early parliamentary elections in Great Britain were held on June 8 at the initiative of the head of the government, Teresa May, who chose to dissolve the parliament in order to strengthen the parliamentary majority before the start of negotiations with Brussels on Brexit.
The PM has made clear she wants support from her "friends and allies" in Northern Ireland's DUP to secure her administration ahead of the Queen's Speech on 19 June.
"She needs to be more collegiate, seeking the advice of the cabinet and backbench MPs while reducing her nearly total reliance on a tiny cadre of advisors". It was later reported that Chancellor Philip Hammond was among the Ministers who had kept notes.
Not long after, a Tory spokesman said that Hill had also resigned.
But, she's since performed a U-turn and chose to form a minority government.
Ms Davidson, who is gay and plans to marry her partner in the near future, said she had received "categoric assurance" from Mrs May about the sanctity of LGBTI rights in Scotland where - unlike in Northern Ireland - equal marriage is legal in the event of any deal with the DUP.
Prime minister warned her authority would be damaged if senior figures were not held accountable.