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At the centre of the battle were Redstone's daughter, Shari, and Philippe Dauman, the chief executive of Viacom - and it appears that Shari has emerged victorious.
The Wall Street Journal, New York Times, and Los Angeles Times are among those reporting that Dauman will step down as chief executive of Viacom, the company that controls Hollywood studio Paramount Pictures and TV channels including MTV and Comedy Central.
Dauman - who has been a key Redstone lieutenant for more than 30 years - will stay on as non-executive chairman until September 13, while chief operating officer Tom Dooley will become interim chief executive. Dauman is set to receive a $72 million golden goodbye, according to reports.
The changes were ratified at a Viacom board meeting late on Thursday night, the reports said, and will need court approval in order to end legal tussles in Massachusetts, Delaware, and California.
The conflict was ignited in May after Dauman was removed from the trust that will control Redstone's assets when he dies or is declared incompetent. He was also ousted from the board of National Amusements, the group that controls Redstone's media empire.
Lawyers representing Redstone cited dissatisfaction with Viacom's recent performance as reason for the decision, but Dauman claimed that the media mogul was being unduly influenced by his daughter, Shari.
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His departure is seen as a victory for Shari Redstone, with the Wall Street Journal reporting that the settlement completes her "stunning rise." She is now the favourite to take control of her father's empire, which also includes CBS.
As well as a $72 million payoff, Dauman has secured another concession. He will be allowed to present proposals to the Viacom board for his ambition to sell a 49% stake in Paramount Pictures. The plan will require unanimous agreement from Viacom's directors.
Viacom is yet to make an official announcement and a spokesman in the