The Scot's departure was announced on Wednesday night, just 24 hours after the 2-0 loss to fellow strugglers Hull City dropped them into the relegation zone.
First-team coach Scott Marshall and goalkeeping coach Andy Marshall have been put in temporary charge for Sunday's FA Cup tie with Leicester City at Villa Park.
In a statement, Villa said: "The club would also like to place on record its thanks to Paul and take this opportunity to wish him every success in the future.
"The club will announce a new manager in due course.
"There will be no further comment from the club at this stage."
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