Brooks has faced criticism from various quarters as she was editor of the News of the World when its journalists allegedly hacked the phone of murdered schoolgirl Milly Dowler.
News Corp shut down the 168-year-old Sunday tabloid last week following various other allegations of phone hacking, including families of victims of the 7/7 London terrorist attacks and the relatives of British soldiers killed on duty.
Announcing her resignation, Brooks said that she felt "a deep sense of responsibility" for the people who have been hurt by the phone hacking scandal, and said she wanted to "reiterate how sorry I am for what we now know to have taken place".
She had wanted to lead News International through the hacking scandal, but recognised that she had become the "focal point of the debate".
In a statement, News International chairman James Murdoch thanked Brooks her 22 years of service to the company.
"She has been one of the outstanding editors of her generation and she can be proud of many accomplishments as an executive. We support her as she takes this step to clear her name," he said.
Murdoch reiterated that an independent Management & Standards Committee would now investigate the scale of phone hacking and criminal behaviour at News International.
He said that the body has been given "direct governance and oversight from News Corporation board members", and its codified standards "will be clear and enforced".
In a momentous week, Rupert Murdoch's media giant opted to withdraw its offer to acquire the 61% of pay-TV giant Sky on Wednesday following pressure from the government.
James Murdoch said that the decision to drop the takeover bid was "a strong signal that our top priority in the UK is to address the issues facing News International".
Tom Mockridge, the chief executive of Sky Italia, has already been named as Brooks's successor at News International. He is in London now and will start straight away.
"Tom is a highly respected and accomplished media executive who has served as chief executive of Sky Italia since its launch in 2003," said Murdoch.
"Tom, who has also been in charge of our European Television business, started his career as a newspaper journalist in New Zealand and he has held a range of top roles in the newspaper industry. The creation of TG-24, Italy's only truly independent 24-hour news channel, is a credit to Tom's leadership and integrity."
News International will this week run adverts in all of its national newspapers apologising to the nation for the phone hacking scandal. Murdoch said that this will be followed by further actions in the future "to address the wrongdoing that occurred".
Brooks, Rupert Murdoch and James Murdoch have all agreed to appear before the Commons Culture, Media and Sport Committee next Tuesday to answer questions about phone hacking. James Murdoch said that the session will give them a chance to show their "determination to put things right".
In a message to News International staff, he added: "The company has made mistakes. It is not only receiving appropriate scrutiny, but is also responding to unfair attacks by setting the record straight.
"I would like to conclude by saying thank you. Throughout this time, you have gotten out great papers every day and have stayed focused. I am deeply grateful for that."