Mr Murdoch could resign as early as in the next few hours, according to Sky News.
In just a few weeks the House of Commons Culture, Media and Sport Select Committee is due to release its findings into reporting practices at the News of the World.
It is also understood Mr Murdoch and his father Rupert, chief operating officer of News Corporation, have both been called to give evidence to the Leveson Inquiry later this month.
A bit of background about James Murdoch.
Born in London in 1972 as one of three children from Rupert's second marriage to Anna, James had an unusual start to his career.
At Harvard University he drew cartoons for the satirical magazine Lampoon and also set up a hip-hop record label, Rawkus, in the mid-1990s.
The company was making a small profit when it was bought by News Corporation and James returned to the family business as head of the firm's music division.
James earned his father's confidence and in 2000 he was appointed chairman and chief executive officer of News Corporation subsidiary Star TV.
BREAKING: Former News International executive chairman James Murdoch has stepped down as chairman of satellite broadcaster BSkyB, the company said.
More background on James....He proved himself in the tough Asian pay TV market by rapidly improving the Hong Kong-based company's fortunes. Star moved into profit after building a strong presence in India and won "landing rights" in mainland China.
But cries of nepotism greeted his appointment in November 2003 as chief executive of BSkyB - the youngest head of a FTSE 100 company.
LATEST: Mr Murdoch is expected to remain on the board of BSkyB as a non-executive director.
Mr Murdoch, who relinquished his role as NI executive chairman in February, said in a letter outlining the reasons for his departure he did not want his role as chairman to become a "lightning rod" for BSkyB.
BREAKING: It has been confirmed that Mr Murdoch will be replaced
by deputy chairman Nick Ferguson.
Mr Murdoch leaves the position just weeks before a Government report is published into reporting practices at the News of the World and an expected appearance alongside his father Rupert, News Corp chief operating officer, at the Leveson Inquiry.
Mr Murdoch's departure comes despite receiving backing from BSkyB shareholders, who reappointed him at the company's annual general meeting last November.
Mr Murdoch also recently stepped down from the boards of auctioneer Sotheby's and pharmaceutical firm GlaxoSmithKline.
BREAKING: Tom Mockridge, chief executive of NI, which publishes The Times, the Sunday Times and the Sun, as well as the News of the World (NotW) before it was shut down, will replace Nicholas Ferguson as deputy chairman.
QUOTE: "I deeply appreciate the dedication of my many talented colleagues at News International who work tirelessly to inform the public and am confident about the tremendous momentum we have achieved under the leadership of my father and Tom Mockridge." - James Murdoch
QUOTE: "With the successful launch of The Sun on Sunday and new business practices in place across all titles, News International is now in a strong position to build on its successes in the future." - James Murdoch
REACTION: Jack Irvine, a former editor of the Scottish Sun, tells the Press Association: "I think it's a tragedy for James Murdoch himself in that he has actually been a very good chairman of BSkyB. Normally one would be quitting a job because you hadn't done a very good job but he is quitting because of what other people have done.''
Mr Irvine believes Mr Murdoch's next step would be influenced by his expected appearance at the Leveson Inquiry and the Culture, Media and Sport Select Committee's report on phone hacking.
Mr Irvine said he believed Mr Murdoch would "get a kicking'' from the committee, but added: "Don't forget he is a young guy and American businessmen in particular can be very forgiving of people's mistakes.''
QUOTE: More from the Labour leader: "He's taken the decision that he has, but what now needs to happen is that the police investigation takes its course and gets to the bottom of exactly what happened. The most important thing is that the organisation has a top-to-bottom clean-up and understands what happened and gets rid of those people who did wrong."
QUOTE: "With his vision, drive and strategic insight, the company has performed exceptionally. The board's support for James and belief in his integrity remain strong." - Nick Ferguson on his predecessor
Don Foster, co-chair of the backbench Liberal Democrat culture committee, says: "James Murdoch will hope this resignation takes some of the pressure off News Corp's bid for BSkyB. No doubt the other BSkyB owners will be breathing a sigh of relief that the bid, for now, seems to be on the back burner."
Mr Foster adds: "However, whether or not News Corp qualifies as a 'fit and proper person' remains to be seen, and there are still unanswered questions on James Murdoch's knowledge of phone hacking. It is essential that this resignation does not act as a barrier to finding out the truth.''
QUOTE: "James has ensured the challenger spirit ... is ingrained in the company's DNA and I am confident Sky's employees, along with Nick [Ferguson], Jeremy [Darroch] and the entire board, will continue to strongly develop the business in the interests of all shareholders." - Tom Mockridge on his elevation
QUOTE: "Two years ago the Murdochs were courted by all and sundry and now James Murdoch is running away with his tail between his legs, frightened of what the Culture Media and Sport Select Committee may say about his disastrous and incompetent running of News International.'' - Labour MP Chris Bryant, a leading campaigner against phone hacking
Mr Bryant added: "The important message for the whole political class is that we should never kow-tow to a media mogul again, nor allow any one person to have such a stranglehold over the British media.''
LATEST: Asked about his reaction to Mr Murdoch stepping down, PM David Cameron said: "Well, it's obviously a matter for him, and a matter for the company - and of course its shareholders."
Shareholder lobby group Pensions & Investment Research Consultants called for Mr Murdoch to leave the BSkyB board entirely.