The departure of Dominic Cummings from Downing Street could give Boris Johnson a "fresh start", say Conservative MPs.
A number of Tory backbenchers have welcomed news the prime minister's chief adviser will step down this year.
It comes after the PM's director of communications, and close ally of Mr Cummings, Lee Cain, resigned.
Ex-minister Theresa Villiers said the pair had been "dismissive" of Tory MPs, and she hoped their replacements would be "more collegiate" with the party.
Mr Cummings confirmed to the BBC's political editor, Laura Kuenssberg, late on Thursday that he would leave No 10 before Christmas.
He said reports that he had threatened to quit in solidarity with Mr Cain had been "invented" - instead pointing to a blog post from January where he wrote he wanted to make himself "largely redundant" by the end of 2020.
Mr Cummings and Mr Cain were both key members of the Vote Leave campaign for leaving the EU before entering Downing Street with Mr Johnson.
The confirmation of their exits come during the final stages of trade talks between the UK and the bloc.
But No 10 said it would not affect negotiations and the government's approach remained "unchanged".
The events of the past 48 hours feel like a political explosion, with Dominic Cummings now confirming his departure from Downing Street by the end of the year.
But while it's tempting to see this is as a dramatic and sudden eruption, it has been a longer-term burn.
The prime minister's chief adviser stepped back somewhat from some of the brutal day-to-day politics he had helped create after the election.
He had been spending more time focusing on trying to rewire Whitehall - trying to increase the importance of science and data in government - hoping to be less involved in the moment-by-moment political rush.
But given his profile, and his nature, was that ever a realistic plan?
Since taking the job at Number 10, Mr Cummings has not been a popular figure with everyone within the governing Conservative Party.
He was known for making disparaging comments about some of Mr Johnson's own MPs, including labelling Brexiteers "useful idiots".
Ms Villiers, who was environment secretary until February, welcomed the upcoming change of personnel.
She told BBC News: "I do feel these changes... are an opportunity for a fresh start, to enable the prime minister to build bridges with some of the backbenches who have become anxious about some of the direction the government has gone over recent months
"There is no doubt that both Dominic Cummings and Lee Cain were pretty dismissive of backbenchers, and on some occasion ministers and secretaries of states as well, and I don't think that was helpful."
The Conservative chair of the liaison committee of senior MPs, Sir Bernard Jenkin, said Mr Cummings' departure was an "opportunity to reset how the government operates and to emphasise some values about what we want to project as a Conservative Party in government".
He told BBC Radio 4's Today programme it was time to restore "respect, integrity and trust" between No 10 and Tory MPs, which he said had been "lacking in recent months".
And fellow Tory Sir Roger Gale called the chief adviser's exit as "an opportunity to muck out the stables" and get a new team in.
He called for Mr Cummings to go "immediately", telling BBC News: "People who campaign well are not necessarily people who can run the country well.
"I believe that what the prime minister needs and deserves is a serious heavyweight political adviser behind him, who understands the scene, understands the system, knows where the bodies are buried."
Who is Dominic Cummings?
- Born in Durham, Dominic Cummings, 48, went to a state primary school before being privately educated at Durham School. He graduated from Oxford University with a first-class degree in modern history
- A longstanding Eurosceptic, he cut his campaigning teeth as a director of the anti-euro Business for Sterling group and once ran a successful campaign to oppose a regionally elected assembly in north-east England
- In Westminster, he worked for Iain Duncan Smith when he was Conservative Party leader and Michael Gove at the Department for Education
- He ran the pro-Brexit Vote Leave campaign in the EU referendum and was behind the group's "take back control" slogan
- After Boris Johnson became prime minister in July 2019, he hired Mr Cummings to be his senior adviser
- Six months later the pair's "Get Brexit Done" campaign message helped the party win a large majority in the general election
- Mr Cummings became more of a public figure following controversy over him making a trip to the north of England when non-essential travel was banned at the height of the coronavirus lockdown
Transport Secretary Grant Shapps told BBC Breakfast he was "not particularly surprised" by the announcement, adding that "advisers come and go over a period of time".
Asked if the departure of Mr Cummings and Mr Cain suggested the prime minister was intending to follow a very different path, Mr Shapps said the PM had "always taken advice from a very wide range of people and doesn't always side with the same people at the end of that decision-making process".