A statement from Publicis Groupe, which owns the agency, said that Roberts will step down on 1 September, "prior to his retirement date due in May 2017".
Roberts hit headlines over the weekend after he said "the fucking debate is over" in an interview with Business Insider when talking about women in leadership positions.
In a statement, Roberts said:
"Fail Fast, Fix Fast, Learn Fast" is a leadership maxim I advocate.
When discussing with Business Insider evolving career priorities and new ways of work/life integration, I failed exceptionally fast.
My miscommunication on a number of points has caused upset and offense, and for this I am sorry.
I have inadvertently embarrassed Saatchi & Saatchi and Publicis Groupe, two companies I love and have been devoted to for almost 20 years.
I have expressed my regret and apology to the companies for the furor my remarks and language stimulated, and I extend this to colleagues, staff and clients.
So that we can all move forward, I am bringing forward my May 1, 2017, retirement from the company, and will leave the Groupe on September 1, 2016.
There is a lot of learning to reflect on, and within the thousands of tweets, comments and articles there are many powerful and passionate contributions on the changing nature of the workplace, the work we do, what success really looks like, and what companies must do to provide women and men the optimal frameworks in which to flourish.
I believe that new thinking, frameworks and measures are needed to make more rapid progress on diversity in all its forms, in all professions and occupations. Hopefully, the focus on this serious and complex issue will gather momentum.
Roberts started his career in the late 60s with London fashion house Mary Quant. He became a senior marketing executive for Gilette and P&G in the Middle East.
At 32, he became chief executive of Pepsi-Cola Middle East in 1982 and then five years later became Pepsi's CEO in Canada. Then in 1989 he moved to Auckland to become chief operating officer with Lion Nathan.
He became the worldwide chief executive at Saatchi & Saatchi in 1997 and was promoted to executive chairman two years ago, based in New York.
The 66-year-old is well-known for his 'lovemarks' philosophy at Saatchi & Saatchi which centres on an emotional connection with brands. His book on the topic explored why some brands are popular over others.