Murdoch was the head of his father Rupert Murdoch's newspaper publisher when the hacking affair engulfed the News of the World.
This is the first time that a member of the Murdoch family has appeared at the Leveson since it was set up last year.
Rupert Murdoch, the chairman and chief executive of News Corporation, is due to appear at the inquiry on Wednesday and Thursday this week.
James, the billionaire's younger son, is likely to be quizzed today on whether he was aware that allegations of phone hacking at the News of the World went beyond just royal reporter Clive Goodman, who was jailed for the crime in 2007.
Last year, he told MPs on the Commons culture select committee that he had no knowledge of the scale of wrongdoing at the newspaper, which was shut down last July.
However, in December an email dated from 2008 emerged indicating that Murdoch had been copied into a message chain referring to the practice as being "rife" at the News of the World.
Murdoch then wrote to the MPs on the committee to admit that he had been copied into the email, but that he had not read the chain in full, meaning he did not see the warning.
He has since stood down as executive chairman of News International, the owner of The Sun, The Times and The Sunday Times. He has also quit as chairman of pay-TV giant Sky, which is 39.1% owned by his father's News Corp.
Yesterday, head of Sky News John Ryley admitted that the broadcaster had 'broken the law' by hacking into personal email accounts for stories, but said that it was "highly unlikely" it would do it again.
> Ofcom to investigate Sky News email hacking