Prime Minister David Cameron believes Rebekah Brooks took "the right decision" in quitting as chief executive of News International in the wake of the phone-hacking scandal at the News of the World, Downing Street said today.
The former Sun and News of the World editor announced her resignation this morning in an internal email to staff at the company, which also publishes The Times and Sunday Times.
Ms Brooks, 43, said she quit to avoid distracting attention from News International's efforts to "fix the problems of the past".
She stood down at the end of a fortnight of increasingly bad headlines for News International since it was revealed that reporters hacked the mobile phone of murdered teenager Milly Dowler while she was editor - though she denies any knowledge of the wrongdoing.
Ms Brooks is still expected to appear alongside News Corporation chairman Rupert Murdoch and his son James for a grilling on the scandal by MPs on the Commons Culture Committee next week.
Reports suggest that she offered to resign at least twice over the past weeks, but was turned down by Mr Murdoch senior. Her position was made more difficult when Mr Cameron said last Friday that her resignation should have been accepted.
Asked what the Prime Minister thought of her departure, Mr Cameron's official spokesman told reporters: "He thinks it is the right decision."
Mr Murdoch has stood by Ms Brooks very publicly since flying into London on Sunday to take personal control of the crisis at News Corp, appearing smiling by her side and describing her as his top priority.
But unconfirmed reports today suggested his daughter Elisabeth had criticised her for damaging the company, while News Corporation's second-biggest shareholder, Saudi Prince Al-Waleed bin Talal, told BBC2's Newsnight that if she was shown to be involved in wrongdoing, then "for sure she has to go".
Ms Brooks wrote in her email to staff: "My desire to remain on the bridge has made me a focal point of the debate.
"This is now detracting attention from all our honest endeavours to fix the problems of the past.
"Therefore I have given Rupert and James Murdoch my resignation. While it has been a subject of discussion, this time my resignation has been accepted."
She said her resignation would allow her the time to give her full co-operation to the police investigation into phone hacking and police bribes, the judge-led inquiry launched by Mr Cameron, and her appearance before the Culture Committee on Tuesday.
Ms Brooks used her farewell message to praise Rupert Murdoch's "wisdom, kindness and incisive advice" and his son James's "great loyalty and friendship".
She was replaced as News International chief executive by Tom Mockridge, who has been chief executive of News Corp's Italian satellite broadcasting arm Sky Italia.
Labour leader Ed Miliband welcomed Ms Brooks's departure, but said it was clear that Rupert Murdoch still did not "get it" about the need to apologise.
"It is right that Rebekah Brooks has finally taken responsibility for the terrible events that happened on her watch, like the hacking of Milly Dowler's phone," said Mr Miliband.
"But as I said when I called for her resignation 10 days ago, this is not just about one individual but about the culture of an organisation.
"Rupert Murdoch says that News Corp has handled these allegations 'extremely well'. He still hasn't apologised to the innocent victims of hacking. He clearly still doesn't get it."
Deputy Prime Minister Nick Clegg said Ms Brooks's resignation was an "important first step in cleaning up this mess".
But he added: "People still need answers. She owes it to the victims of phone hacking and the country at large to explain her role in what happened."
James Murdoch revealed that News Corp plans to use adverts in this weekend's press to "apologise to the nation".
News Corporation's chief executive in Europe said he and his 80-year-old father would also use next week's appearance before MPs on the Culture Committee to "speak to them directly about our determination to put things right".
In a message to News International staff, James Murdoch hailed Ms Brooks as "one of the outstanding editors of her generation" who "can be proud of many accomplishments as an executive".
But he added: "The company has made mistakes. It is not only receiving appropriate scrutiny, but is also responding to unfair attacks by setting the record straight."
Meanwhile, Rupert Murdoch took a more defiant tone in saying he will use Tuesday's committee hearing to challenge "total lies" made about his media empire.
In an interview with the Wall Street Journal, which is owned by News Corp, Mr Murdoch senior said News Corp had handled the crisis "extremely well in every possible way", making just "minor mistakes".
He said the company would now establish an independent committee, headed by a "distinguished non-employee", to investigate all charges of improper conduct.
Asked whether the Prime Minister agreed with Mr Murdoch that only "minor mistakes" had been made, Mr Cameron's official spokesman said: "Clearly there have been mistakes made. There are a lot of questions to answer."
Pressure on the Murdochs intensified with the disclosure that the FBI has opened an inquiry into claims that News Corp journalists sought to hack the phones of the victims of the 9/11 terror attacks.
Congressman Peter King, chairman of the House Homeland Security Committee who asked the FBI to investigate, said it was the "American dimension" of the phone-hacking scandal.
"This could be a criminal matter. The FBI handles criminal investigations," he said.
Meanwhile, Scotland Yard was also under pressure to explain how it came to employ a former News of the World journalist arrested yesterday in the phone-hacking investigation as a PR consultant.
Neil Wallis, 60, who was deputy editor under Andy Coulson's editorship, was detained in a dawn raid on his west London home and questioned for several hours at Hammersmith police station.
While he was being held, the Yard was forced to admit that it had paid him £24,000 to work as a two-days-a-month public relations consultant. His contract was cancelled less than six months before the Operation Weeting investigation into phone hacking was launched.
Home Secretary Theresa May fired off a letter to Metropolitan Police commissioner Sir Paul Stephenson demanding an explanation.
The commissioner will now give evidence to the Commons Home Affairs Committee, which is looking at the police investigation, on the same day the Murdochs appear.
Michelle Stanistreet, general secretary of the National Union of Journalists, said: "This is too little too late. We all know she has worked hand-in-glove with James Murdoch and they are equally culpable.
"This will be cold comfort to the hundreds of journalists who have lost their jobs at the News of the World."
The Hacked Off campaign for victims of phone-hacking said in a statement: "All the victims we have spoken to have told us that they cannot see how Rebekah Brooks could remain in her job given what has so far been revealed.
"The key issue is not however whether Rebekah Brooks is in work, but whether she lied to Parliament, told the full truth to the police or was engaged in a massive cover-up. That is what we want the victims want to know."
Lord Prescott ridiculed Mrs Brooks' claim that her "desire to remain on the bridge had made me a focal point of the debate".
"I was a seafarer of 10 years, I wouldn't have liked her on the bridge if she didn't know what was going on or where she was going and what direction, and that is why she has gone," he told the Lords.
He added: "All these others are small bit players, it's Mr Murdoch (senior), he is the spy in the middle of this net and if we don't deal with him he will just come back to the same old practices."
A close aide of Lord Prescott suggested that what he was trying to say was "spider in the middle of this web".
Mark Lewis, the solicitor representing murdered schoolgirl Milly Dowler's family, said he was pleased Mrs Brooks had resigned.
He added: "News International, News of the World, had ruined people's lives.
"In a sense it is the chicken coming home to roost. It is time. Every dog has its day and Rebekah Brooks, I suppose, is that dog."
Sara Payne, the mother of murdered schoolgirl Sarah, and fellow child welfare campaigners at Phoenix Chief Advocates, Shy Keenan and Fiona Crook, said it was "right" that Ms Brooks had quit.
In a brief statement, they said: "Given the circumstances, this was the right and proper thing for her to do.
"Our thoughts today are with Milly and her family and we can make no further comment on an ongoing investigation."
Rupert Murdoch was driven past photographers as he left News International's Wapping offices in a black Land Rover shortly after 3.30pm.