Mr Murdoch, who was appointed BSkyB chairman in December 2007, said: “I have been privileged to serve first as chief executive and then as chairman of this outstanding company and I am proud of what we have achieved over this period.
“As attention continues to be paid to past events at News International, I am determined that the interests of BSkyB should not be undermined by matters outside the scope of this company.
“I am aware that my role as chairman could become a lightning rod for BSkyB and I believe that my resignation will help to ensure that there is no false conflation with events at a separate organisation.”
The parent company, News Corporation, said in a statement that Mr Murdoch was leaving UK newspapers following his relocation to the company’s headquarters in New York, and would concentrate on television and international operations.
And last month, Mr Murdoch said in a letter to the Department for Culture, Media and Sport (DCMS) Committee that he accepted he was partially to blame for not uncovering phone hacking at the News of the World.
That committee is reportedly considering censuring him for failures to fully investigate allegations that accessing the voicemail message of celebrities and others was widespread at NI.
Media regulator Ofcom is likely to extend its inquiry into Mr Murdoch if the parliamentary committee finds against him.
It is considering whether he remains a “fit and proper” person to oversee an organisation with a licence from the regulator.
Mr Murdoch’s successor as BSkyB chairman, Nick Ferguson, said: “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.”