Thompson will work alongside the Droga5 leadership teams in London and Sydney, as well as maintaining her role as chief executive of the New York office.
Bauer will also continue to hold his role as chief strategy officer in New York, with an expanded global remit.
According to a Droga5, the global promotions are a result of an influx of new business. The agency won ten new accounts in 2014. The global focus will also help support existing clients looking to expand in international markets.
Thompson joined Droga5 in 2008, two years after it was founded, from Bartle Bogle Hegarty New York. She was promoted to chief executive from her role as president within two years at the agency.
Bauer joined the same year as Thompson, also defecting from BBH New York. He rose from head of strategy to his current role as chief strategy officer in 2012.
Following Dundas's departure, the agency announced it would be parachuting in Nick Simons, the senior account lead, from the New York office to become Europe managing director.