The 52-year-old returns to the npower Championship to take charge of a Robins side that has won just six times this season and is six points adrift of safety.
The club parted company with manager Derek McInnes on Saturday night after 15 months in charge at Ashton Gate on the back of a 4-0 home defeat to Leicester.
And the City board moved quickly to appoint the former Doncaster boss who turned down fellow strugglers Barnsley last week.
O'Driscoll, who has signed a 12-month rolling contract, was relieved of his duties at Forest on Boxing Day after just five months in charge, a decision which shocked many in football.
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."
John Lansdown, the Robins' football managing director, added: "Sean has got a really good record at clubs and a record of being there for the long term and we appointed Sean because we believe he has the ability to keep us up this season. We are looking forward to working with him for a long time."