The 56-year-old will stand down from his role with immediate effect as the club currently sit 22nd in the League One table after taking 15 points from 18 games.
Vice-chairman Jon Lansdown wrote in an email to supporters: "We have given the situation as much time as we could to improve but have become increasingly concerned about the club's league position and have decided that a change of head coach will give the club the best possible chance of improving this.
"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."
Lansdown has also insisted that the club will not rush to appoint a new head coach following O'Driscoll's dismissal.
John Pemberton will take charge for Saturday's trip to Preston North End.