It follows a scandal over phone hacking at News Corp's UK newspaper group.
News Corp deputy chairman Chase Carey said the bid had become "too difficult to progress in this climate".
The scandal has already led to the closure of the UK's biggest-selling newspaper, the News of the World.
On Friday, Prime Minister David Cameron announced details of a public inquiry into phone hacking and media regulation.
Market reaction "We believed that the proposed acquisition of BSkyB by News Corporation would benefit both companies, but it has become clear that it is too difficult to progress in this climate," said News Corp deputy chairman and president Chase Carey in a statement.
"News Corporation remains a committed long-term shareholder in BSkyB. We are proud of the success it has achieved and our contribution to it."
BSkyB's share price briefly dropped following the announcement, taking it down 4% for the day, before recovering to close 2% up.
End QuoteThere could be further damage to the reputation of News Corporation, damage which could alienate advertisers and buyers of its newspapers and entertainment”
'Huge humiliation' A spokesman for Mr Cameron welcomed the news: "As the prime minister has said, the business should focus on clearing up the mess and getting its own house in order."
The Labour leader, Ed Miliband, called it "a victory for people up and down this country who have been appalled by the revelations of the phone hacking scandal and the failure of News International to take responsibility".
Liberal Democrat deputy leader Simon Hughes said that "the sun is now setting on the Murdoch empire".
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News Corp already owns 39% of BSkyB, but may be compelled to give up even this minority stake if it is deemed not to be "fit and proper" by regulator Ofcom following the conclusion of current police investigations.
Robert Peston added there had been "a lot of speculation" that Mr Murdoch might now want to sell his UK newspapers, but the current state of the industry made them less attractive to potential buyers.
"The question is, who is going to pay him the price that they are worth? He will not want to sell those papers at a loss."
Mr Cable, who was secretly recorded last year saying he had "declared war" on Rupert Murdoch, had been in charge of overseeing the bid, but was replaced by Culture Secretary Jeremy Hunt.
Public inquiry Mr Cameron has asked Lord Justice Leveson to oversee a public inquiry into the News of the World scandal and media regulation.
In a statement to the Commons, he said the inquiry would begin as "quickly as possible" and would be in two parts - an investigation of wrongdoing in the press and the police, and a review of regulation in the press.
The judge will have powers to call media proprietors, editors and politicians to give evidence under oath, the PM said.
Mr Cameron said those who sanctioned wrongdoing should have no further role in running a media company in the UK.
Scope of hacking inquiry
- Culture, practices and ethics of the press
- Their relationship with the police
- Failure of current regulation
- Contacts made and discussions between national newspapers and politicians
- Why previous warnings about press misconduct were not heeded
- Issue of cross-media ownership
Mr Cameron told MPs he would require all ministers and civil servants to record meetings with senior editors and media executives to help make the UK government "one of the most open in the world".
Mr Miliband welcomed the proposal, arguing it must be imposed retrospectively, so that he and Mr Cameron publish all details of meetings with media executives dating back to the last general election.
The prime minister was previously criticised for meeting Rupert Murdoch, head of News Corporation, in Downing Street soon after the election, because Mr Murdoch did not walk through the front door.
Newspapers which did not support the government ran stories of "secret meetings".
Who is Lord Justice Leveson?Lord Justice (Sir Brian) Leveson became a barrister in 1970 and a QC 16 years later.
The 62-year-old was made a High Court judge in 2000 and appointed to the Court of Appeal in 2006. He was senior presiding judge there from 2006 to 2009 and now, as chairman of the Sentencing Council, is responsible for criminal sentencing policy in England and Wales.
Lord Justice Leveson is well known for being the barrister who led the prosecution case against serial killer Rose West, who was jailed in 1995 for the murder of 10 women and girls.
He was also the judge during the 2006 trial over the murder of 10-year-old London schoolboy Damilola Taylor.
Mr Cameron responded: "She was right to resign, that resignation should have been accepted. There needs to be root and branch change at this entire organisation.
"What has happened at this company is disgraceful - it's got to be addressed at every level."
In other developments:
- News International's legal manager Tom Crone, who primarily worked at the News of the World and on the Sun, has left the company
- The Sun has defended its story revealing Mr Brown's youngest son Fraser had cystic fibrosis. It has released a video of the man it says was the source - the man's face is not revealed and his voice is disguised to protect his identity
- The prime minister met the parents of Milly Dowler, after which they welcomed news of the phone hacking inquiry
- The Australian arm of Mr Murdoch's media empire is to investigate all payments made to contributors since 2008
- In the US, Senate Commerce Committee chairman Jay Rockefeller called for an investigation into whether phone hacking targeted any American citizens and whether journalists working for News Corp had broken US law
- Shares in News Corp have fallen 14% since 4 July, wiping about $5bn off the company's value
The former Conservative deputy chairman Lord Ashcroft makes the allegations in a blog posting on ConservativeHome, which he owns. Mr Baldwin has not responded to the claims.