The Championship club announced on Monday that 48-year-old Robinson will start work on March 1.
He watched Bristol beat Rotherham at the Memorial Stadium on Sunday, with the west country club remaining on course to make this season's promotion play-offs.
Robinson resigned as Scotland boss following a dismal autumn series earlier this season that culminated in a defeat against Tonga after losses to New Zealand and South Africa.
But Bristol chairman Chris Booy has been in discussion with the ex-Bath and England flanker for several weeks, culminating in Monday's announcement.
Robinson was a member of England's coaching staff under Sir Clive Woodward during the successful 2003 World Cup campaign, and then he succeeded Woodward in the top job between 2004 and 2006.
He has also coached Bath and Edinburgh, leading Bath to the 1998 Heineken Cup final, when they beat Brive in Bordeaux to be crowned European champions.
"I am delighted to be joining Bristol Rugby at such an exciting time for the club," Robinson said. "I firmly believe that with the passion for rugby in the region and the vision of the owners, Bristol has the potential to be one of the most successful sides in England.
"I am looking forward to building a squad with a blend of experience and young, home-grown talent, to play an exciting and winning brand of rugby.
"Our immediate objective is to achieve promotion back to the Aviva Premiership as soon as possible."
- Sports & Recreation
- Bristol Rugby