This Sunday's edition of the News of the World will be its last, News International chairman James Murdoch has said, after days of increasingly damaging allegations against the paper.
The 168-year-old tabloid is accused of hacking into the mobile phones of crime victims, celebrities and politicians.
On Thursday, the Met Police said it was seeking to contact 4,000 possible targets named in seized documents.
Its editor Colin Myler said it was "the saddest day of my professional career".
He added that "nothing should diminish everything this great newspaper has achieved".
The News of the World, which sells about 2.8million copies a week, is famed for its celebrity scoops and sex scandals, earning it the nickname, the News of the Screws.
Downing Street has said it had no role or involvement in the decision to close.
Mr Murdoch said no advertisements would run in this weekend's paper - instead any advertising space would be donated to charities and good causes, and proceeds from sales would also go to good causes.
News International has refused to comment on rumours that the Sun could now become a seven-day-a-week operation.
"What happens to the Sun is a matter for the future," a spokeswoman for News International said. The Sun, another News International tabloid, is currently published from Monday to Saturday.
The spokeswoman also refused to say whether the 200 or so employees at the paper would be made redundant, saying: "They will be invited to apply for other jobs in the company."
The News of the World's political editor, David Wooding, who joined 18 months ago, said it was a fantastic paper.
"They cleared out all the bad people. They bought in a great new editor, Colin Myler, and his deputy, Victoria Newton, who had not been sullied by any of the things that had gone on in the past.
"And there's nobody there, there's hardly anybody there who was there in the old regime."
The Guardian says that Andy Coulson, formerly David Cameron's director of communications, will be arrested on Friday morning over suspicions that he knew about, or had direct involvement in, the hacking of mobile phones during his time as editor of the News of the World.
The Guardian also says that a former senior journalist at the paper will also be arrested in the next few days.
There have been repeated calls for Rebekah Brooks - the former editor, now News International's chief executive - to resign. But in an interview Mr Murdoch stood by her again, saying he was satisfied with her conduct.
In a statement made to staff, Mr Murdoch said the good things the News of the World did "have been sullied by behaviour that was wrong - indeed, if recent allegations are true, it was inhuman and has no place in our company".
"The News of the World is in the business of holding others to account. But it failed when it came to itself."
He went on: "In 2006, the police focused their investigations on two men. Both went to jail. But the News of the World and News International failed to get to the bottom of repeated wrongdoing that occurred without conscience or legitimate purpose.
"Wrongdoers turned a good newsroom bad and this was not fully understood or adequately pursued.
"As a result, the News of the World and News International wrongly maintained that these issues were confined to one reporter.
"We now have voluntarily given evidence to the police that I believe will prove that this was untrue and those who acted wrongly will have to face the consequences. This was not the only fault.
"The paper made statements to Parliament without being in the full possession of the facts. This was wrong.
"The company paid out-of-court settlements approved by me. I now know that I did not have a complete picture when I did so. This was wrong and is a matter of serious regret."
He said: "So, just as I acknowledge we have made mistakes, I hope you and everyone inside and outside the company will acknowledge that we are doing our utmost to fix them, atone for them, and make sure they never happen again.
"Having consulted senior colleagues, I have decided that we must take further decisive action with respect to the paper. This Sunday will be the last issue of the News of the World."
He reiterated that the company was fully co-operating with the two ongoing police investigations.
He added: "While we may never be able to make up for distress that has been caused, the right thing to do is for every penny of the circulation revenue we receive this weekend to go to organisations that improve life in Britain and are devoted to treating others with dignity."
The BBC's political editor, Nick Robinson, said that Rupert Murdoch has sacrificed the News of the World - or, at least, its title - instead of the chief executive of News International, Rebekah Brooks.
"Team Murdoch must have realised that it would be referred to again and again over the next few months in connection with the alleged phone-hacking of a murdered girl, grieving parents and war widows," he said.
"The question now is whether this will make the government's dilemma about the takeover of BSkyB easier or harder."
Mark Pritchard, secretary of the influential Conservative backbench 1922 committee and vice-chairman of the parliamentary media group, has told the BBC he wants the government to delay a decision on the BskyB takeover.
"The government should take the political and moral lead - and announce a delay to the BSkyB decision until all outstanding legal impediments have been removed," he said.
Labour MP Tom Watson told Sky News it was "a victory for decent people up and down the land, and I say good riddance to the News of the World".
But Justice Secretary Ken Clarke said: "All they're going to do is rebrand it."
And former deputy prime minister Lord Prescott, who alleged his phone was hacked, thought the decision was simply a gimmick.
In April, the News of the World admitted intercepting the voicemail messages of prominent people to find stories.
It came after years of rumours that the practice was widespread and amid intense pressure from those who believed they had been victims.
Royal editor Clive Goodman and private investigator Glenn Mulcaire were jailed for hacking in January 2007 after it was found they targeted Prince William's aides.
Detectives recovered files from Mulcaire's home which referred to a long list of public figures and celebrities.
The scandal widened this week when it emerged that a phone belonging to the murdered schoolgirl Milly Dowler had also been hacked into, and some messages deleted.
Leading brands, including Sainsbury's, Ford and O2, pulled their newspaper advertising and shares in BSkyB fell on fears that the scandal could hinder parent company News Corp's bid for the broadcaster.
On Wednesday, the government promised an inquiry in the hacking allegations, but the nature of it is undecided.