In her new role Kemp will work alongside Tom Bazeley, the chief executive, to focus on "streamlining the agency’s processes", and will manage finance.
She will continue to work on the Boots and Network Rail accounts.
Kemp has been at the agency since 2010 and managed the integration of Lean Mean Fighting Machine into M&C Saatchi last year. M&C Saatchi bought LMFM in May.
Clare Willetts, a business director at M&C Saatchi, replaces her as a managing partner.
Willetts will work alongside Ed Palmer, also a managing partner, and will report into Bazeley. She will handle the integrated Blue Cross and Doddle accounts, and work for Douwe Egberts.
Bazeley said: "Having looked deeply at the structure of this agency, the team and I believe a smaller, tight-knit management team with clear responsibilities for each element of our output is essential.
"And with Camilla Kemp in the new position of chief operating officer, this will ensure more fluid processes across the agency, while keeping the quality of our creative output at the heart of everything we do.
"Meanwhile, with Clare’s fundamental belief in the importance of the creative product, combined with her commercial experience, I’m confident she’ll help take this agency in the right direction as managing partner.
"Camilla and Clare will be instrumental in terms of how the agency evolves in 2015 and beyond."
M&C Saatchi appointed Bazeley, a founding partner at LMFM, as chief executive in October, following the departure of Camilla Harrisson to Anomaly.
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