Potter will remain on the agency’s global operations committee and partner, alongside global CCO Judy John, chief client officer Lisa Sepulveda, and the regional brand leads led by global chair Amanda Glasgow.
Edelman said that during her four years as EMEA president and CEO Potter has delivered the agency's highest profitability in the region for seven years.
Potter, who was formerly CEO and president of ad agency BBDO, said: "It has been an honour to lead the regional business for the last three years and together with the leadership team see such profitability and impressive work achieved for our clients."
Williams has led Edelman’s UK and Ireland business since October 2011. Under his leadership the business has become the UK's biggest PR agency. Revenue doubled during his tenure - reaching £63.1m in 2018 - as the business grew into areas including corporate advisory, research and polling, and risk management.
Williams previously led corporate affairs and communications for the BBC and Reuters.
"In my new role leading our businesses in Europe, the Middle East and Africa, I intend to deploy a similar strategy - build a unified and focused team that regardless of national borders can intelligently and diligently serve clients across the region," he said.
The agency confirmed it will be completing an extensive search before appointing a successor to Williams.
Both Potter and Williams will assume their new roles from 1 October and will continue to be London-based, reporting to Matt Harrington, global COO, Edelman.
Harrington said: "The process for searching for the right person for these roles has reinforced the quality and breadth of talent we have at Edelman."