Sky, a part of BSkyB, reports that the resignation will be confirmed later Tuesday.
Media mogul Rupert Murdoch's News Corp., which owns 39 percent of BSkyB, had no comment. BSkyB could not immediately be reached.
James Murdoch, one of his father's chief lieutenants, has been under pressure as result of Britain's tabloid phone hacking scandal.
He has been shedding posts to concentrate on his role in his father's television business as News Corp. struggles to shake off the hacking furor that erupted at its now-shuttered tabloid News of the World.
In February, James Murdoch quit as chairman of News International, News Corp.'s British newspaper division.