Philip Angelastro, the company’s controller and senior vice-president of finance will take over the role, having been at the company since 1997.
Weisenburger has been with Omnicom since 1998 and prior to that, spent more than ten years with venture capital and private equity firm, Wasserstein and Co.
His departure comes five months after the Group's failed merger with Publicis.
John Wren, president and chief executive of Omnicom said: "Randy has made significant contributions to the team in building a world-class company during our time together.
"At Omnicom, we place considerable emphasis on succession planning and Randy and I have long agreed that Phil would eventually take over as CFO. I have complete confidence that under Phil’s leadership, Omnicom will continue to build on our long term track record of creating value for all our stakeholders."
Weisenburger said: "I’m proud to have been part of such an outstanding group of people and the consistent success we have shared over many years. I believe the company is extremely well positioned both strategically and financially, to continue to lead the industry for years to come."