The agency will create a campaign encouraging people to offer protection and support for ambulances during an armed conflict. It picked up the business in a competitive pitch against a number of undisclosed agencies.
The ads will target governments that provide permission for the Red Cross to carry out medical missions, military authorities and personnel, and the wider public.
The agency's work will highlight the charity's message that every victim of war has a right to be treated, and that ambulances carrying the Red Cross symbol should have access to the sick and wounded.
The finished campaign will include both TV and print and will run around the world, in existing war zones or at the beginning of hostilities.
Neil Dawson, the founding partner of Hurrell & Dawson, said: "This is an important message, from an organisation that is always willing to speak out with boldness and authority. We are flattered to have been chosen."