O'Driscoll took charge at Ashton Gate in January with the club bottom of the Championship and departs with City in the relegation places in the third tier of English football.
The 56-year-old former Doncaster Rovers manager was unable to prevent City from slipping out of the Championship last season as the club finished bottom.
A run of just two wins from 18 league games this term has prompted the City hierarchy to take action, with John Pemberton set to take charge of Saturday's league clash at Preston North End.
Jon Lansdown, City's vice chairman, said in a statement on the club's official website: "The league table does not lie.
"We are currently in the relegation zone and have been there for most of the season.
"This is not acceptable and the board feels that it needs to take action to try and rectify this; we need to move to ensure that results on the pitch keep up with progress off the pitch.
"It is vital that we now look to appoint a head coach who buys into our strategy and can help us to continue to grow and develop it successfully. This, of course, includes results on the pitch."
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