Symonds joined the team at the end of 2013 as part of a wider restructure that helped lift them from ninth in the constructors' championship to third in 2014. In total the team have scored 14 podiums during Symonds' three-year spell.
Claire Williams, deputy team principal, paid tribute to Symonds' contributions - and said the team will reveal further details about their new technical leadership in 'due course'.
"Pat has been a tremendous asset to this team over the past three years," Williams said.
"Pat’s appointment was the start of a major restructuring exercise, and he has been pivotal in reshaping Williams into what is a much stronger racing team today. I would like to thank him for all of his hard work and commitment during that time.
"We now look to the future and will be announcing details regarding the team’s technical leadership in due course."
Mercedes' technical chief Paddy Lowe, instrumental in the world champions' recent run of success, has been linked with a switch to Williams in the media, while speculation also continues as to where former Ferrari technical director James Allison may end up in 2017.