Mr Mockridge, who has been in the position since July last year, is leaving the company to "pursue new opportunities".
News Corporation chairman Rupert Murdoch said Mr Mockridge's decision to step down was "entirely his own".
BSkyB is the parent company of Sky News.
Meanwhile, News Corporation confirmed it will stop publication of its iPad app, The Daily.
The dedicated subscription news feed, which cost between $19 (£11.80) and $39 (£24.20) a month, was launched in February 2011 to maximise interactive capabilities of iPads.
Mr Murdoch said: "For nearly 22 years, it has been my pleasure to have Tom Mockridge as a colleague.
"Whether it was his early days with our newspaper group in Australia, his incredible work building Sky Italia, or his steadfast leadership of News International, Tom has always been a skilled executive and a trusted friend.
"His decision to step down is absolutely and entirely his own. I am sorry to see him leave us but I know he will be a great success wherever he goes."
Mr Mockridge took over leadership of News International, the publishing arm of News Corporation, from Rebekah Brooks at the height of the phone-hacking scandal.
The ex-newspaper journalist joined News Ltd in Australia in 1991, where he worked with James Murdoch, deputy chief operating officer of News Corporation, at Star TV, before moving to his native country of New Zealand, where he oversaw the company's newspaper and TV operations.
Last week, Mr Mockridge backed calls for a "tough" new press watchdog but warned that state-backed regulation would put too much power in the hands of politicians.
He said: "As a company we are keen to play our full part, with others in our industry, in creating a new body that commands the confidence of the public.
"We believe that this can be achieved without statutory regulation - and welcome the Prime Minister's rejection of that proposal.
"We accept that a new system should be independent, have a standards code, a means of resolving disputes, the power to demand prominent apologies and the ability to levy heavy fines."
Mr Mockridge said he was "genuinely shocked" about the allegations of phone-hacking at the company.
But he insisted The Sun would not be shut down like its now defunct Sunday sister paper, The News Of The World, if more allegations emerged.
More From Sky News