BSkyB's board confirmed that Murdoch would stay on as company chairman, despite the phone-hacking scandal at News International, of which he is also the chairman.
"There was a long discussion as you would expect at the board on Thursday around governance, and that included the role of chairman, and the outcome was that the board was unanimous in its support for James as chairman," BSkyB chief executive Jeremy Darroch told BBC News.
However, one unnamed board member told BBC that the decision to back Murdoch could not be seen as being forever.
If evidence were to emerge that damaged the credibility of Murdoch then the board would have to reconsider whether he needed to stand down.
BSkyB's shares tumbled following the phone-hacking controversy. The company has now decided to return 1 billion pounds to shareholders angered by the recent fall in share prices.
Operating profits, excluding earnings from non-core activities such as investments, rose 23 per cent to 1.07 billion pounds, while pre-tax profits fell 15 per cent to 1.01 billion pounds.
Murdoch withdrew a bid under intense public and political pressure to takeover BSkyB in which his company current holds 39 per cent stake.