Robinson was confirmed as the side's new director of rugby on Monday and is set to take up his new role on March 1, with a return to the Aviva Premiership the goal he wants to achieve "over the next couple of years".
The 48-year-old watched Bristol beat Rotherham at the Memorial Stadium on Sunday, with his new role at the West Country club his first since he resigned as Scotland boss earlier this season after a dismal run of form. However, following discussions with Bristol chairman Chris Booy over the past few weeks, Robinson said: "I am really excited about getting back into rugby."
He added: "I was at the game (against Rotherham) and it is a tough Championship.
"It was great to see the way the ball was moved around and the attacking prowess that was there. This (league) is an important step to get to the Premiership and the belief that I have that we can achieve at Bristol.
"I am looking forward to achieving that with Bristol over the next couple of years. It is a step by step process, it just doesn't happen overnight, and working with the culture that is here and building on that is something really exciting."
Robinson was a member of England's coaching staff under Sir Clive Woodward during the successful 2003 World Cup campaign before landing the top job between 2004 and 2006. After his time with England, the former flanker had two seasons at Edinburgh before being appointed Scotland's head coach in 2009.
Bristol, who are backed by Guernsey-based millionaire Steve Lansdown, are looking to regain Premiership status next season, although Newcastle remain firm Championship title favourites
Bristol chairman Booy said: "Since Steve Lansdown has become involved with the club (during the 2008-09 season) we have been very serious about where we want to be, but it has been difficult to attract the right players and somebody like Andy.
"This appointment shows that we are serious. We want the best people to do the best jobs, and that is not just director of rugby, but also players. Andy's appointment shows that we are going to get there, and there are no more ifs, but it's when."