Hunt originally joined Sheffield Wednesday on loan from Crystal Palace in the summer of 2015, before he made the permanent switch away from Selhurst Park the following January.
The 27-year-old has made 108 appearances for the Owls.
He becomes Bristol City's fifth signing in what has been a busy summer transfer window.
'Sky Sports' reported that the deal was worth around £1.6million.
Manager Lee Johnson told Bristol City's website: "I think Jack is an excellent acquisition for us. He is very experienced in the Championship and he is of a good age where he is coming into his prime.
"He is a very tough competitor, he's physically fit and he likes to maraud forward.
"The signing gives us strong competition in that back line and that's where we need to be because it's a tough division with many, many games.
"We are delighted to bring in a player of his quality and we look forward to welcoming him into the Bristol City family."
Hunt will be joining fellow signings Adam Webster from Ipswich, Andreas Weimann from Derby, Marley Watkins from Norwich and Hakeeb Adelakun from Scunthorpe.
July 6, 2018