The former world champions, who have not scored a point in their last seven races, said in a statement that O’Driscoll would guide the long-term future of the team and report to founder Frank Williams and the board.
The newly-created role of group CEO unites the F1 team and Williams Advanced Engineering under one management structure.
“This new role strengthens the company and will help us achieve our goals both on the race track and in diversification,” said Williams, who recently appointed his daughter Claire as his deputy.
“Working with Claire, I am in no doubt that the future of Williams is in safe hands.”
O’Driscoll, who was managing director of Jaguar cars from 2007-2011, has been a non-executive director of Williams since 2011.