Burns was the worldwide account director on General Mills and had been with the Publicis Groupe-owned agency for 25 years.
The General Mills account includes brands such as Cheerios, Yoplait, Pillsbury and Green Giant and has billings of more than $600m.
Saatchi & Saatchi said: "While the recent departures are unfortunate, we remain confident in our ability to service this important client. We will continue partnering them to create big ideas that transform General Mills' brands and take the business to even greater heights."
Burns was the joint chief executive of Saatchi & Saatchi New York until last September. Executive creative director Tony Granger and Arnold Worldwide's Mary Baglivo took over the running of the agency, leaving him to step back to the role of managing the General Mills account.
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