The News Ltd. takeover offer would give Murdoch's global media empire control of a large slice of Australia's pay television industry.
The move was supported by James Packer, whose Consolidated Press Holdings owns half of Consolidated Media.
News has offered $3.50 Australian dollars for each Consolidated Media share, valuing the company at AU$1.97 billion ($2 billion). The deal would give News a 50 percent stake in pay TV operator Foxtel and full ownership of Fox Sports in Australia.
The offer remains subject to approval from the Australian Competition and Consumer Commission and the Foreign Investment Review Board.
The News Corp. board must also approve the deal.
News Ltd., which owns 70 percent of Australia's newspapers, also announced a major restructure to centralize its Australian operations and reduce duplication.
News chief executive Ken Williams told staff that there would be redundancies, but he did not say how many.
The announcement came two days after Fairfax Media Ltd., Australia's No. 2 newspaper publisher, said it would cut 1,900 jobs over three years and erect pay walls for the websites of two of its flagship newspapers.
The organization would be reduced from 19 operating divisions to five, including three covering the Australian east coast where News Ltd. earns 80 percent of its revenue.
Williams said the company and advertisers continued to value printed newspapers. News Ltd. sells around 11 million newspapers a week to Australia's population of 23 million.
"We believe in print and are committed to print," he said in a video address to staff.