The move comes ahead of the departure of Mike Mathieson.
As part of the changes, Jim Dowling, the managing partner at Cake since 2008, will become the managing director of Cake in the UK.
Pettett and Dowling take up their new positions on 1 December.
Pettett, who will be the last co-founder left at the agency, said: "These are exciting times at Havas as it continues to invest in data and content.
"The opportunities for Cake to play a front and centre role in a truly joined-up network are greater than ever."
Cake works with brands including Shop Direct, Sainsbury’s, Sony, Microsoft and Virgin Atlantic.
Mathieson, a co-founder and the current chief executive at Cake, is leaving the agency at the end of the year to launch a music consultancy called Harmonic.
The third co-founder of Cake, Mark Whelan, became a global creative director at Havas Worldwide in July last year.