Cobbold, 32, is currently a partner at TBWA, where he has spent the past year managing the agency's McCain business.
His appointment strengthens the agency's senior-level account handling following the departure of Tanya Livesey, who recently moved to Rainey Kelly Campbell Roalfe/Y&R.
At TBWA, Cobbold also handled the Eurostar and Congestion Charge accounts, as well as working on the launch of 3.
Nick Howarth, the managing director of HHCL, said: "We've been looking for a client services director for some time and I'm delighted to get someone of Jason's calibre."
In his capacity as partner, Cobbold also worked to develop closer links between TBWA and Omnicom, initiating and implementing TBWA+, a partnership scheme to drive integrated solutions for clients.
Before joining TBWA, two-and-a-half years ago, Cobbold was an account director at BMP DDB.
Cobbold said: "I was most impressed by the energy and vision of the team at HHCL. I'm delighted to be joining the agency and becoming part of the story. This is a great opportunity."