FHF saw off competition from Brands2Life, Citigate Dewe Rogerson, Blue Rubicon and Headland, which also pitched for the work.
Fishburn had worked with CCI since 2010, before the agency's merger with FleishmanHillard.
CCI reviewed its comms requirements at the end of 2015, and created the new brief focusing on promoting the company to support sales and marketing efforts across its European, Asian and Australasian markets.
The FHF team, led by deputy CEO Ali Gee and director Judith Moore, started work on the contract this month. They will deliver a campaign that "brings to life the advertising medium’s creativity and effectiveness, highlighting CCI's innovation advancements, including the international expansion of its digital out-of-home network", the agency said.
CCI chief customer and revenue officer, Stefan Lameire, said: "During a closely fought pitch process, FHF demonstrated sharp customer insight, had strong strategic thinking, huge energy and some creative, highly actionable campaign ideas.
"These ideas will help us demonstrate the scale of our ambition for outdoor as digital innovation continues to drive the transformation of the world’s oldest advertising medium, reinforcing its ability to allow brands to reach and engage today’s connected consumer in a more impactful way."
Gee said: "Clear Channel International has been a longstanding client and we have enjoyed a very successful partnership over this time. The new brief enables us to build on this and we look forward to working with the team to deliver an exciting campaign built on some truly groundbreaking creative."
It follows CCI rival JCDecaux handing its PR account to Propeller, and FHF winning two other international clients earlier this month.