The 49-year-old signed a three-and-a-half-year contract with the Robins on Tuesday.
Cotterill takes charge of City with the team two points adrift of safety in the standings.
"The challenge is one I'm looking forward to," he told the club's official website.
"Having done a bit of coaching last season it's not really where I see myself. I see myself very much as a manager who can coach, rather than a coach who can manage.
"I hope I can deliver what the fans want, which is success out on the pitch. It certainly won't be for the lack of trying. I'll bring passion with it, that's for sure, and hopefully they'll take to me."
Cotterill will sit in the dugout at Ashton Gate for the first time on Saturday when City take on Rotherham United in the league.