In a letter to the board Murdoch said: "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.”
Nicholas Ferguson who joined as a director in 2004 and became deputy chairman in 2010 will succeed Murdoch as chairman and News International chief executive Tom Mockridge will take on the role of deputy chairman.
News Corp’s bid for control of BSkyB was dropped after the scandal blew up last summer and in February Murdoch stepped down as News International's chairman.
News International, the group's newspaper arm, owns The Sun and was the publisher of the now closed News of the World, the paper at the centre of the hacking storm.
Murdoch added: "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.
Ferguson said: “The board's support for James and belief in his integrity remain strong. We understand his decision to step aside at this time and we both welcome and look forward to his continued contribution as a non-executive director.”
BSkyB shares fell 3 pence to 677 pence.