The company's board met with Murdoch under mounting pressure over the phone hacking scandal in Britain.
The person familiar with the decision says the role of the chairman had been discussed at length, and Murdoch received the unanimous support of all directors. That is expected to be confirmed in a statement.
The board meeting was the first since News Corp. abandoned a takeover bid for BSkyB because of the scandal at the tabloid News of the World.
British newspapers fall within James Murdoch's responsibilities as CEO and chairman of the international division of News Corp.