Paddy Lowe has officially left Williams after what was described as an extended leave of absence following the team's poor start to the season.
"After a period of careful reflection, I have reached the decision that I will not return to work at Williams," the former chief technical officer said.
A Williams statement said Lowe had stepped down with immediate effect.
Deputy team boss Claire Williams said she "understood and respected" his decision.
Lowe's "leave of absence" from Williams was announced in March, following the team's failure to get a car ready for the start of pre-season testing and the discovery that it was the slowest in the field by a considerable margin.
Williams, who dominated Formula 1 for periods in the 1980s and 1990s, are on average more than two seconds a lap slower than the next slowest car this season.
Lowe was brought on board at the start of 2017, after three years leading the dominant Mercedes team's technical department, and charged with returning the team to competitiveness.
But the 2018 car was the slowest in the field and this year's has fallen back significantly further.
Since Lowe stepped down, Williams have been undertaking a thorough review of how they ended up in such a difficult position, and what to do about turning their fortunes around.
Claire Williams said at the Monaco Grand prix last month: "I definitely feel that we can see some light at the end of the tunnel now.
"We all know that it takes time to bring performance to your car. There's definitely a lot of good work going on back at the factory that people may not necessarily be seeing yet.
"The aerodynamics team are doing a great job finding performance in the tunnel and we're going to be bringing that to races over the coming weeks and months with a package coming mid-way through the season that we will hope will bring some significant performance to us."