Dawe is currently deputy chief executive of VisitBritain, before which her role was director of communications.
Last year she moved over to handle purely London 2012 initiatives, while Patricia Yates became head of strategy and insight.
Dawe joined the British Tourist Authority from the London Tourist Board in 1991. Her early career included working for the Book Marketing Council and the BBC World Service.
Christopher Rodrigues will now relinquish his executive responsibilities and revert to the role of chairman.
Dawe was awarded the MBE in 2008 for services to tourism.