The 25-year old Australian international has agreed a three-year deal with the Robins after his contract at Elland Road expired at the end of last season.
City boss Keith Millen said it was a great capture and was delighted to welcome the former Birmingham City man to Ashton Gate.
“We're delighted he has agreed to join us as we've been following him for a little while," Millen told the club's official website.
"Leeds United offered him a new contract and there were other Championship clubs showing interest but he's opted to join us.
"He's a passing midfielder with a great range and he demands the ball. He's a good age and an Australian international who has played a big part in Leeds' success in recent years.
"He's excited from speaking to him and he likes what he has heard about the club. He wants to help us get into the Premier League.
"There aren't many creative midfielders available so the search has been difficult. The top players cost a lot of money but we've been fortunate in getting him on a free transfer."