The Grove outfit has also announced that acting team principal Simon Roberts will take on the job full time.
Roberts will report to Capito, who will in turn report to Dorilton boss and Williams chairman Matthew Savage.
The 62-year-old Capito has a busy CV, having worked for several manufacturers and F1 teams in a variety of roles.
A former motorbike racer and Paris-Dakar participant, he worked at BMW in the late 1980s as a powertrain development engineer, before moving to Porsche in a motorsport management role in 1989.
He joined Sauber in 1996 as a member of the managing committee, becoming chief operating officer two years later. He was with the Swiss team for five years as it developed relationships with the likes of Ford, Petronas and Red Bull.
He joined Ford in October 2001 as director of special vehicle engineering, and spent a decade with the company in various jobs, eventually becoming director of global performance vehicles and motorsport business development.
In May 2012 he became head of Volkswagen Motorsport, overseeing the successful WRC programme, before moving to McLaren as CEO in September 2016. However he stayed with the Woking team for just five months before departing.
Capito then returned to Volkswagen in June 2017 to run its R performance car division, before leaving in October.
"It's a great honour for me to join Williams Racing during these exciting and demanding times for both the team and for F1," Capito said.
"It is an honour to be a part of the future of this storied team, and one that carries such a poignant name in the sport, so I approach this challenge with great respect and with a huge amount of relish."
Savage added: "He is an experienced and competitive individual, who has built winning teams and is a winner in his own right.
"He understands the Williams heritage and will work well with the team in pursuit of our objective to return to the front of the grid."