Simon Bolton, the chief executive of JWT London, confirmed that the agency would be recruiting externally to replace King, who is due to leave at the end of May.
She will relocate to New York to head Kraft across 64 countries, reporting to the network's worldwide chief executive, Bob Jeffrey.
Replacing the retiring Ron Burns, her brief is to continue the expansion of Kraft brands across the globe.
Bolton said: "This is a great job for Ros. It suits her marketing and client skills.
"Her enthusiasm, intelligence and integrity have played a significant part in the revitalisation of the JWT brand in London."
King was promoted to managing director in 2001, following the departure of the agency's then-chief executive Stephen Carter to NTL.
She was subsequently responsible for developing Boots into a multimillion-pound client. However, after a turbulent period, the agency lost the £40m account to Mother last year.
During her career, King spent a total of 10 years at Leo Burnett. She also had a two-year spell at Ogilvy & Mather and ran client services while at McCann-Erickson.
King said: "Being the managing director of JWT is one of the best jobs in London, but being the global business director on Kraft is one of the best jobs in the JWT world. This will be a challenge for me, but I am very much looking forward to it."
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