A team spokeswoman said the Briton had wanted to spend more time with his family and had departed the factory, although his last working day is officially December 31.
Along with technical head Mike Coughlan and aerodynamics head Jason Somerville, Gillan was an important figure in taking Williams back to the top of the podium this year after their worst ever season in 2011.
The team took their first victory in eight years when Venezuelan Pastor Maldonado won the Spanish Grand Prix in Barcelona in May.
By doing so, Maldonado picked up five times as many points in one race as Williams had managed in all of the previous season when they finished ninth overall.
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