Robertson co-founded the UK-based not-for-profit One Young World with support from Havas in 2009, with a mission to empower young leaders all over the world. She will continue as a consultant at the company through to the end of next year.
During her time at Havas, Robertson led the UK division in serving global clients including Barclays, RB and Jaguar. She led the acquisition of Work Club in 2014.
Andrew Benett, the global chief executive of Havas Worldwide, said Robertson has "contributed considerable value" to the company.
David Jones, the former chief executive and a co-founder of One Young World, quit in January 2014 and Chris Pinnington, the global chief operating officer, left in July that year.
At the same time, the network has made a string of high-profile hires, including Sean Lyons from R/GA as the global chief digital officer and Chris Hirst, the chief executive of Grey London, to lead European operations.