Dauman was a longtime associate of former Viacom CEO Sumner Redstone, whom he replaced as chairman in 2016. He served as a member of Viacom's executive committee from 1994 to 2000, supervising Paramount Pictures Entertainment, Showtime Networks, and Simon & Schuster.

Viacom was spun off from CBS in 1971 due to new FCC rules banning TV networks from owning syndication companies. Under Viacom, Baruch started cable networks Showtime and Lifetime, and acquired the rights to MTV, Nickelodeon, VH1, and more. He is also a co-founder of C-SPAN.

The second incarnation of Viacom lasted from 2005 to 2019, when it merged with CBS Corporation to form ViacomCBS. It was then transferred to Paramount Global, the majority shareholder of which is National Amusements. The president of National Amusements is Redstone's daughter, Shari Redstone.