Unger is director of the strategy, international, technology and economist group at the regulator.
He will step into the new role at the end of the year when current chief executive Ed Richards steps down after eight years running Ofcom. His departure was announced in October.
Ofcom said it is in the throes of recruiting a full-time replacement for Richards, with an appointment set to be announced in 2015. Unger will be in charge until that person joins the regulator.