Brooks left the company under a cloud four years ago at the height of the phone hacking scandal, but was cleared of all charges last year.
Her re-appointment to the role was rumoured over the weekend, although News Corp said this week it was still in talks with Brooks.
Her appointment came as part of a massive management shake-up which also included the appointment of Tony Gallagher, the former editor of the Telegraph, as editor-in-chief of the Sun.
Meanwhile, Mike Darcey, the company's current chief executive, will step down after three years in the role, while current Sun editor David Dinsmore will become News UK's chief operating officer.
In a statement today, Robert Thomson, News Corp's chief executive, said:
Rebekah will lead a great team at News UK into the digital future, while maximising the influence and reach of our newspapers, which remain the most informative and successful in Britain and beyond. Her expertise, excellence and leadership will be crucial as we work to extend our relationship with readers and advertisers, and develop our digital platforms to take full advantage of our brilliant journalism.Tony Gallagher is one of the most respected journalists and editors in the UK, with a long and honorable history with the Daily Telegraph group and the Daily Mail. His integrity and his ingenuity are splendid assets for The Sun across the week.