Baillie (above) will be based in London and takes the job title of head of client service, engagement disciplines, EMEA. He will report to UK and EMEA CEO Colin Byrne, and chief digital officer Chris Perry.
His hire comes at the same time as the German office of what is the world's second largest PR firm welcomes senior hire Bernhard Hofer, formerly of digital comms group UDG. Hofer takes the role of head of Engagement Engine operations.
Both will join the agency in January.
Weber Shandwick defines its engagement disciplines as the work done by its creatives, analysts, planners, content creators and social media strategists.
The firm refers to the work of these teams as its Engagement Engine - and has been ramping up this proposition as a marketing concept in recent months.
Baillie has been at the digital agency FullSix since the start of 2014. It was acquired by Havas Group in September 2015. His time at FullSix followed eight months leading the agency Hello People, of which he was one of three co-founders.
Before this he was CEO of Ogilvy & Mather London, and has also worked for ad firms Grey, Saatchi & Saatchi and BBH, with clients including Unilever, American Express, Ford, Motorola, Diageo, British Airways and Gillette.
Hofer, who will be based in Berlin, has nearly two decades of experience in digital campaign project management, with clients including Audi, eBay and Telefónica, according to a Weber Shandwick press release.
Weber Shandwick’s chief digital officer Chris Perry said: "The stakes continue to rise on fusing creative, engagement-driven ideas with new media approaches to capture attention and reach intended communities. As we continue to build and broaden capabilities across EMEA markets, top leadership talent like Hugh will help to shape and deliver how Weber Shandwick answers the call for clients."
Baillie said the firm had "a clear expertise for delivering business results for clients no matter the communications channel".