Baugh, who has been at Heathrow for four years, will start in his new role on 30 March.
He is replacing Vickie Sheriff, who moved to Diageo last year to become global comms director. Scot Marchbank has been covering the position on an interim basis.
Baugh was previously director of airport comms at BAA.
Baugh said: "I can’t think of a more exciting time to be joining the team or to be promoting the role that transport plays in driving UK economic growth."
He has been overseeing PR at Heathrow as the debate on expansion and capacity has intensified. This has included the launch in late 2013 of Back Heathrow, a 'grassroots' campaign aimed at garnering more support for expanding the airport.