Carter had been with the Grove team since May 2016. He was twice the most senior team member present at a track on a race weekend, first when acting team principal Simon Roberts was sidelined by COVID at the 2020 Turkish GP, and again when Capito tested positive prior to last year's Saudi Arabian GP.
In a short statement about his departure, Capito said: "As we look ahead at our engineering strategy and requirements for the next year and beyond, we have made changes in our engineering structure.
"Adam Carter has left the team and I would like to thank him for his hard work and contribution over the last six years."
Williams has undergone several changes of personnel since Dorilton acquired it in September 2020. Capito joined as CEO that December, and then took over the team principal role when Roberts left in July 2021.
Having spent his first months in the company observing and deciding what was missing Capito hired two former VW Motorsport colleagues in key roles.
Francois-Xavier Demaison was named technical director in March 2021, and when Roberts left Demaison also became responsible for trackside and engineering.
In November, Capito added Belgian Sven Smeets, another VW veteran, as sporting director.
As part of the reshuffle, Doug McKiernan, who joined the team in February 2018 and served in a variety of roles including that of chief designer, left last season.
Carter has gained experience with a variety of teams over his two decades in the sport. He started out in a junior engineering role at Arrows in 1998, and after the team closed he joined McLaren as a test team engineer in 2002.
He then had a brief spell at Jordan in 2004 before moving to Renault as a test and race engineer later that year.
In 2008 he joined Wirth Research as chief engineer and race programme manager, before moving to Williams after eight years with the company.
He started in 2016 as senior engineer, and was quickly promoted through a variety of jobs, becoming chief of engineer of vehicle programme and chief of staff in 2017, chief engineer and head of design in 2019, and engineering director in 2021.
