His departure marks the end of a relationship that has lasted for just over one season, with De Beer having previously held the same role at F1 rivals Ferrari.
It comes just weeks after Ed Wood left his role as chief designer for personal reasons.
Williams said Chief Engineer Doug McKiernan, who joined the team in Feburary having worked at McLaren for 16 years from 1999, will “assume full responsibility over the aerodynamic and design direction of the car”.
They added: “Dave Wheater is stepping up to take on the role as Head of Aerodynamics.
“The team would like to thank Dirk for his hard work over the past year and wish him the best for the future.”
It has been a difficult season so far for Williams, with the British outfit bottom of the constructors’ championship table on four points.
Their Chief Technical Officer Paddy Lowe said earlier this month Williams understand the issues they have encountered and have put a recovery programme in place.