The two parties have signed a non-binding letter of intent for News Corp to acquire 100% of Shine, and will now jointly apply for regulatory clearance for the deal.
The takeover, on the cards ever since Shine appointed JP Morgan to advise on strategic options last month, will see Elizabeth take a seat on News Corp's board.
She owns around 60% of Shine, producer of shows such as MasterChef, Ashes To Ashes and Spooks, with Sony holding 20% and Sky - which is 39% owned by News Corp - controlling 13%. The remainder is owned by the company's management.
Upon successful completion of the transaction, Shine Group will report to Chase Carey, News Corp's deputy chairman, president and chief operating officer.
"This is a unique and exciting opportunity for us. Shine is a leader in the global television production business with a proven track record of developing hit shows and new formats worldwide," said Carey.
"We have every confidence that Shine will be an important part of the expansion strategy for our worldwide TV operations."
Elisabeth Murdoch, chairman and chief executive of Shine Group, said that the alliance will enable Shine to "continue to lead and prosper" in the rapidly consolidating media industry.
"News Corporation is the partner that enables us to maintain our aspiration to be best in class across all our sectors, and prepares and equips us for future growth," she said.
"Shine shares News Corporation's long-standing belief in creative excellence and ambitious expansion. I could not be happier or more proud that from such modest beginnings Shine will join such an extraordinary group of companies."
Rupert Murdoch, chairman and chief executive of News Corp, added: "Shine has an outstanding creative team that has built a significant independent production company in major markets in very few years, and I look forward to them becoming an important part of our varied and large content creation activities. I expect Liz Murdoch to join the board of News Corporation on completion of this transaction."
The deal comes as News Corp awaits a UK government decision on whether the company's bid to acquire the remaining shares in Sky will be passed to the Competition Commission.