The work is worth $20m (£10.6m) and forms part of a $250m (£130m) revamp by the Trinidad and Tobago government.
Cagney is now planning BWIA's first major UK promotional campaign. It currently runs seven flights a week from Heathrow and Manchester.
Cagney's ad agency Chick Smith Trott will handle advertising, while brand strategy will be run by Brandaid.