Hinton served as executive chairman of the British unit that oversaw News Corp.'s U.K. tabloid newspapers at the heart of the scandal for 12 years.
Hinton said in a statement that he was "ignorant of what apparently happened" but felt it was proper to resign. He apologized for the hurt caused by the actions of journalists who worked for the now-shuttered tabloid, News of the World.
Earlier Friday, News International said CEO Rebekah Brooks had also resigned.
Rupert Murdoch had defended Brooks amid pressure for her to resign and he previously refused to accept her resignation.
Brooks was editor of the News of the World tabloid between 2000 and 2003, including the time when the paper's employees allegedly hacked into the telephone of 13-year-old murder victim Milly Dowler when police were searching for her. That allegedly interfered with the police investigation.
Brooks said the debate over her position as CEO of News International was now too much of a distraction for parent company News Corp. and she would concentrate on refuting allegations in the scandal.
The news of her resignation was greeted with relief. Prime Minister David Cameron says it's the right decision.
After the scandal broke out, Murdoch closed the 168-year-old News of the World and let go of his bid to take full control of British Sky Broadcasting.
Meantime, News Corp. also announced Friday it would run ads in all of Britain's national papers this week to "apologize to the nation for what has happened."
The Associated Press contributed to this story