The Robins parted company with McInnes on Saturday following a 4-0 home defeat by Leicester City which sent the club to the bottom of the Championship.
Coventry City boss Mark Robins was mooted as an early contender for the position, but O'Driscoll has been handed the job of leading the club to safety on a rolling contract.
O'Driscoll was dismissed by Nottingham Forest on Boxing Day after lasting less than six months in charge at the City Ground and turned down a return to management with the Robins' fellow strugglers Barnsley earlier this month.
He was also linked with the Blackpool post following Michael Appleton's departure to Blackburn Rovers last week, but reportedly rejected the Bloomfield Road vacancy in favour of taking charge at Ashton Gate.
O'Driscoll said: "Sometimes you have to go with your gut instinct. It just feels right.
"I think it needs a concerted effort from everyone (to stay up) and I'll get all the credit or blame, but everyone needs to be moving in the same direction.
"We need to hit the ground running and in this topsy-turvy Championship, anything is possible.
"If we put a run together we can soon be in a different position in the league. Everyone I have spoken to is confident we have the ability in the squad to achieve that.
"I like the way the club is being developed. This has always been a well-run football club and that is never going to change."
City's football managing director Jon Lansdown told the club's official website: "It's important that we give ourselves the best possible chance of surviving and moving up the Championship table this season.
"In Sean we have someone with a track record of developing clubs longer term, as well as a wealth of experience at this level, which will be vital in our fight for survival in the Championship.
"I am delighted he decided to join us ahead of a number of other offers he has received.
"This season has been a rocky ride and we find ourselves in a difficult position, but we still have the time and ability to get out of it.
"We need everyone associated with Bristol City Football Club to pull together and get behind Sean, the staff and players to give them every ounce of support possible between now and the final game of the season."