Sir Martin Sorrell, who has been at the helm of the firm for the past 33 years, announced on Saturday evening he was stepping aside.
WPP said that the probe had concluded, adding “the allegation did not involve amounts that are material”.
The 73-year-old said in a statement: “As I look ahead, I see that the current disruption is simply putting too much unnecessary pressure on the business, our over 200,000 people and their 500,000 or so dependents, and the clients we serve in 112 countries.
“That is why I have decided that in your interest, in the interest of our clients, in the interest of all shareowners, both big and small, and in the interest of all our other stakeholders, it is best for me to step aside.”
The company said Sir Martin will be treated as having retired, with chairman Roberto Quarta becoming executive chairman until a new chief executive has been appointed.
Sir Martin denied any wrongdoing after the allegations surfaced earlier this month, but said he understood the company had to investigate it.
He previously worked at Saatchi & Saatchi, and was knighted in the Queen’s New Year honours list in 2000.
He said: “In the coming period, I will be available to the board and any of you, should you want help with anything, anywhere.”.
He added: “As a founder, I can say that WPP is not just a matter of life and death, it was, is and will be more important than that.”