Butler had previously been marketing director at Honda Racing F1, before the team was acquired by Brawn GP earlier this year.
The team's incredible success, which sees driver Jenson Button top the Drivers' standings, has resulted in bargain deals for its first sponsors, including Richard Branson's Virgin Group and leisure brand Henri-Lloyd.
Earlier this month, the cars' livery was used to promote upcoming blockbuster Terminator Salvation starring Christian Bale at the Spanish Grand Prix.
Butler is replaced by Bastien Hibon, formerly creative director at Friends of the Earth.
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