Gillett has said that he is excited at the prospect of playing under O'Driscoll, who managed him previously at Forest and Doncaster Rovers.
"I've worked under Sean a couple of times. He knows what I'm about and I know all about him," Gillett told Bristol City's official website.
"The gaffer says the younger lads have been doing really well and he really rates them. If I can be an older head around them, helping at the same time, then hopefully that can benefit the team.
"I've played mainly as a defensive midfielder under Sean, but really I can play anywhere across the middle and also in behind the strikers. I'm just happy to be here. I want to be playing regularly and hopefully I can do that here at Bristol City. When the offer came up I jumped at it."
Gillett has made two appearances for Forest this season.