A years-long succession battle within Rupert Murdoch's conservative media empire has drawn to a close, with his son Lachlan set to control the news group.

The deal, which the family announced on Monday, will ensure the ongoing conservative leaning of Fox News, The Wall Street Journal and The New York Post even after 94-year-old Rupert's death.

Under the agreement Lachlan will control a new trust while siblings Prue MacLeod, Elizabeth Murdoch and James Murdoch will cease being beneficiaries of any trust with shares in Fox or News Corp.

It follows years of tension between the media mogul and three of his children over the future of the family-owned newspapers and television networks.

The Murdoch family's internal turmoil served as inspiration for the hit television drama Succession. The deal announced on Monday - the finale of the real-life saga - ends all litigation over the family's trust.

Lachlan's more politically moderate oldest siblings are poised to sell their holdings in Fox and News Corp in the coming months. They will also be named as beneficiaries of a new trust, which will receive cash from the sale of about 14.2 million shares of News Corp. and 16.9 million shares of Fox Corp.

The sale of their shares will add to the three siblings' existing inheritance, but prevent them from having any influence over the political bent of the family's media conglomerate.James has in recent years distanced himself from his family's business, citing disagreements over editorial content.

Lachlan is currently the chair of News Corp, which counts The Wall Street Journal and The Times among its slew of publications. He is widely seen as the most politically conservative of Rupert's oldest children.

"The leadership, vision and management by the company's chair, Lachlan Murdoch, will continue to be important to guiding the company's strategy and success," News Corp said in a statement announcing the deal.

Of Rupert's six children, the oldest four have been implicated in the legal turmoil over the company's future. His younger children from his marriage to Wendi Deng Murdoch, Chloe and Grace, are also named as beneficiaries in the new family trust.

The battle over control of the media empire played out largely behind closed doors in Nevada, a state that offers unusual privacy for family trust disputes, after Rupert took the surprising step of attempting to alter the terms of the family's trust.

He wanted to ensure his empire would fall solely into Lachlan's hands rather than to all four of oldest children, but in December last year a Reno court rejected that bid saying Rupert and Lachlan had acted in "bad faith" in trying to amend the trust.

Monday's deal was a "mutual resolution of the legal proceedings", according to the companies.