The pitch, which was open to both BBC roster and non-roster agencies, also included Rainey Kelly Campbell Roalfe/Y&R at an earlier stage.
Fallon will be responsible for producing a campaign to promote the World Service's programming that will break in the latter half of the year.
It will mark the first major marketing push by the global radio network for six years.
It is understood that the campaign will include TV and radio spots as well as print, outdoor and online. It will seek to remind UK audiences of the value of the BBC World Service, and build awareness among younger listeners.
The World Service, a non-profit station, launched in 1932 and is funded by grant-in-aid through the Foreign and Commonwealth Office by the British Government.
It broadcasts in 32 lang-uages to weekly audiences of around 183 million people.