Wright, who made 205 for Preston over the past eight years, has signed a two-and-a-half-year contract with Bristol and has an option for a further 12 months.
The 24-year-old Socceroos defender passed a medical and trained with his new team-mates ahead of their FA Cup third round clash with Fleetwood Town on Sunday morning (AEDT), where he could make his club debut.
"Bailey has a warrior spirit and represents a good signing for us," Bristol coach Lee Johnson told the club's website.
"He's 24 and has great Championship experience; he's tough, an Australian international - an old-fashioned stopper."
VIDEO: Watch Bailey Wright's first interview on #BristolCity Player HD now. https://t.co/dzg5JKHF5D pic.twitter.com/pzMH33mWhI — Bristol City FC (@bcfctweets) January 6, 2017
Last month, Preston coach Simon Grayson indicated he was keen for Wright to sign a new deal with the club and said he "owes the club a lot".
Capped 12 times for Australia, including scoring on his international debut against Saudi Arabia, Wright was part of Preston's elevation to the Championship after winning the League One play-offs in 2014-2015.