Verklin will stand down from the board with immediate effect and will hand over his day-to-day responsibilities, but will remain available to Aegis Media for a number of months.
US reports have tipped him to take a role leading Project Canoe, which is a consortium of cable operators attempting to create a set of universal metrics for video-on-demand.
Verklin, who has worked at Aegis Media for almost 10 years, said: "I have had the privilege of establishing Aegis Media from scratch across the Americas. Many of the most interesting times of my career have come in the past decade, in a marketplace changing almost by the hour.
"However, Aegis Media has a long pedigree in driving change and revolution. I have watched Sarah go from strength to strength in our business over the past 10 years, and I know that Aegis Media will scale new heights under a new generation of leaders."
Fay will immediately take the new position of chief executive of Aegis Media North America, responsible for the US and Canada.
Latin America becomes a separate business unit, reporting directly to Mainardo de Nardis, chief executive of Aegis Media Global. The Latin America division quadrupled its revenue last year and now has more than 500 people, managing many of Aegis Media's international clients across the region.
It helped Aegis Media Americas, which includes agencies Carat, Vizeum, Isobar, Posterscope and Velocity, earn about $300m in revenue last year.
Nardis said: "David has put Aegis Media on the map in the Americas. Under his leadership we have built a diversified marketing communications business, with digital and media at its heart.
"With Sarah Fay at the helm of our North American agencies, we have a leader who is strong, practical and universally admired.
"She has been groomed for this job over the years and I have no doubt that, together with a strong management team, she will successfully lead us through the next phase of development in North America."
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