Former Hull and Newcastle forward Hatem Ben Arfa will not be able to play for Nice this season under FIFA rules.
Hull are in talks to sign Aaron Lennon on loan from Tottenham for the rest of the season, Sky sources understand.
Cotterill was a free agent after a short spell working on the coaching team at QPR under Harry Redknapp earlier this season.
The 49-year-old returns to management almost 18 months after leaving his last post at Nottingham Forest and succeeds another former City Ground boss in O'Driscoll, who oversaw the Robins' relegation to League One and subsequent poor start in the third tier.
Bristol City vice chairman Jon Lansdown said: "I'm delighted that Steve has chosen to join Bristol City Football Club.
"I believe he has the drive, energy and ability to get us back to winning ways.
"He is passionate about bringing success to this club and I am looking forward to working with him to achieve that."
O'Driscoll was in charge at Ashton Gate for just 10 months and left with the team 22nd in the Sky Bet League One table, having managed only two wins in 18 matches this season.
The 56-year-old oversaw just 11 victories during his 40 games at the helm.
Cotterill began his managerial career with a two-year spell at Sligo Rovers in Ireland, whom he led into Europe.
In 1997 he was presented with the chance to manage his hometown club Cheltenham and he led the Robins from the Southern League Premier Division to the Football League and promotion to League One.
Spells in charge of Stoke and Burnley followed before Cotterill won the League Two title with Notts County in 2010.
He then took over at Portsmouth, a club in crisis after relegation from the Premier League, but kept Pompey in the Championship during his 15 months in charge before leaving the south-coast club to join Forest.
The Reds were in struggling in the Championship when Cotterill took over from Steve McClaren in October 2011 but he led the club clear of trouble.
Cotterill's first game in charge of Bristol City will be a potentially hazardous FA Cup second-round tie at Conference outfit Tamworth in front of the television cameras this Sunday.