Rupert Murdoch’s News Corp. will swap its controlling stake in the satellite TV broadcaster DirecTV Group Inc. with Liberty Media Corp. in exchange for Liberty’s 16 percent stake in News Corp., the companies announced Friday.

The deal, word of which leaked two weeks ago, settles a dispute between Murdoch, News Corp.’s chairman and CEO, and Liberty’s Chairman John Malone, who surprised Murdoch two years ago by suddenly building up a large stake in the global media conglomerate that Murdoch built.

Under the deal, News Corp. will give Liberty its 38.4 percent stake in El Segundo-based DirecTV, three Fox regional sports cable networks and $550 million in cash.

In return, News Corp. will receive Liberty’s entire stake in News Corp., which is worth 16.3 percent of the company’s value. News Corp. said in a statement that the deal will amount to a buyback of about $11 billion of its own stock.

The deal is subject to various regulatory approvals and must also be approved by a majority of the holders of News Corp.’s Class B voting shares, excluding the Murdoch family and Liberty.