Lowe had been on an extended "leave of absence" since March 5, before the start of the season.
"After a period of careful reflection I have reached the decision that I will not return to work at Williams," he said in a team statement.
Lowe's position at the former world champions appeared shaky last year and worsened after they failed to finish their new car in time for the start of testing in Barcelona and turned up two days late.
The team are last in the championship and have yet to score a point with a car that has been the slowest on track all season.
Williams finished last overall in 2018 and have not won a race since 2012.
Lowe joined Williams in 2017 from dominant champions Mercedes but last year's car - the first under his supervision - proved ill-handling and uncompetitive.
The family-owned British team have British rookie George Russell and Poland's Robert Kubica as their drivers.
"We understand and respect the decision Paddy has reached and wish him well for the future," said deputy principal Claire Williams.
(Reporting by Alan Baldwin; Editing by Hugh Lawson)
