Right-back Hunt joined on a two-year deal last week to end his 10-year stint with the Trotters.
Hunt failed to make a single appearance in the last two seasons with Wanderers and the 26-year-old is relishing the prospect of a new start at Ashton Gate.
He told the club's official website: "It's fantastic for me to get away as I had found chances difficult to come by at Bolton in recent times.
"When you have a manager who really wants you to play for your team it's always very refreshing.
"The move has come at just the right time as I am desperate to get back to playing football again at a massive club like Bristol City."