The £4.3 billion terminal, which was unveiled by the Queen last Friday, will open its doors to passengers on 27 March.
The Dewynters campaign will run for 12 months on six high-resolution digital dis-play screens in the international and domestic arrivals baggage halls. The advert-ising will feature video footage of upcoming theatrical productions, as well as static imagery.
The sites can be updated remotely and will change frequently to promote different shows. They can also target the arrival of particular flights with language-specific ads.
The 40-inch screens, installed specifically for the theatrical agency, will advertise upcoming local shows as well as productions that have a global franchise such as Les Miserables and The Phantom of the Opera.
Janice Fernandes, the UK business development director of JCDecaux Airport, said: "It's fantastic to have such a great consumer brand at the airport, using these new digital airport panels to their full potential.
"Dewynters' campaign will be unmissable, reaching the entire arriving audience with creative that can be updated as often as required."
JCDecaux Airport has invested £25 million in digital and poster advertising sites in Terminal 5, the largest deployment of digital outdoor in any airport worldwide.