Autosport said that Gillan, who joined Williams in 2011, had left them to "spend more time with his family".
With a background in aerodynamics, Gillan had previously worked in Formula 1 for McLaren, Jaguar/Red Bull and Toyota.
The Northern Irishman also held a professorship at the University of Surrey, and it was from there he was lured by Williams in September 2011.
The team, nine-times World Constructors' Champions, were in the process of shaking up their technical department at the time as they sought to boost their competitiveness.
Williams finished a lowly ninth in the 2011 standings but with Gillan joined by the likes of new Technical Director Mike Coughlan and Head of Aerodynamics Jason Somerville, they enjoyed a better season in 2012.
Results were still inconsistent, meaning that Williams finished only one place higher in the overall standings.
However, the team's Renault-powered FW34 was much-improved upon its predecessor and with Pastor Maldonado driving, the team scored their first win since 2004 in the Spanish Grand Prix.