Symonds, who has left his role as technical consultant to Marussia to join Williams on August 19, has been brought in as Williams still search for their first point of the season.
Team principal Frank Williams said: "I'm delighted that Pat is joining the team.
"His technical capabilities and sporting successes speak for themselves and I'm sure that his knowledge and leadership will contribute considerably to the success that all of us at Williams are working hard to achieve."
Symonds, who comes to Williams as chief technical officer, has worked in F1 for 30 years, achieving championship success with Michael Schumacher at Benetton and Fernando Alonso at Renault.
"Williams is a team steeped in success and engineering excellence and I'm honoured to be asked to play a role in returning the team to its rightful place at the pinnacle of F1," said Symonds.
"Sir Frank, Mike (O'Driscoll) and Claire (Williams) have put in place the foundations for success and I'm immensely excited to begin this new challenge."
Symonds said of his time with Marussia: "I have thoroughly enjoyed my time with the Marussia F1 Team over the course of the past two and a half seasons.
"The team has developed immeasurably during that time and it now has all the right people and resources in place to achieve great things in the future. I wish the team the success it so richly deserves."
Marussia team principal John Booth added: "We would like to thank Pat for the contribution he has made to the development of that structure. We look forward to announcing plans for our continued growth when it is appropriate to do so."
Williams group chief executive officer Mike O'Driscoll said Symonds had been brought in to return Williams to the winner's enclosure.
O'Driscoll said: "Williams' sporting and engineering heritage dictates that we secure the finest talent available.
"Pat brings unrivalled technical and managerial skills in addition to a proven ability to deliver on track results.
"Our commitment to return Williams to winning ways is absolute and this appointment is yet more evidence of our collective desire to return the team to the position is deserves."
Coughlan had been brought into Williams in 2011 and last season contributed to the team's first win since 2014 when Pastor Maldonado took victory in Spain.
But this season Maldonado and Valtteri Bottas have so far failed to pick up a single point.
A Williams statement said of Coughlan: "The team thanks him for the significant contribution he has made since 2011 and wishes him well in his future endeavours."