Viacom Inc. has named Bob Bakish, a 19-year company veteran who has spent the past decade leading its international channels, as its acting president and chief executive following the departure of interim CEO Tom Dooley in November.

The Viacom board approved the promotion of Mr. Bakish, currently CEO of Viacom International Media Networks, at its board meeting on Monday, according to people familiar with the matter. The company previously announced that Mr. Dooley would depart on Nov. 15.

The...