The start-up, founded last year by Fallon's Matt Keon, Jonathan Trimble and Tim Millar, pitched against several agencies including Bartle Bogle Hegarty and Saint.
In the past, the British Library has worked with a number of agencies including Rainey Kelly Campbell Roalfe/Y&R, which won a project from the library in 2008.
18 Feet will now take on all the advertising for a two-year campaign targeted at engaging younger people, with a view to using their input to create a landmark exhibition at the library as part of the 2012 Cultural Olympiad.
The campaign will span digital, experiential and traditional advertising channels and will break in London in October before rolling out nationwide in January 2011.
The British Library is the latest of London's attractions to begin planning advertising activity in the run-up to the 2012 Olympics, in a bid to take advantage of the increased flow of visitors to the city.
The win bolsters 18 Feet's client list, which includes its founding client Freeview, as well as the global make-up brand Avon.