The 28-year-old, who has signed a three-year contract, has joined Wolves for an undisclosed fee. Hull turned down a £5million bid for the Republic of Ireland international in January.
Hunt told the club's official website: "I'd like to say thanks to Hull for being so understanding with the deal. I had a good year there and would like to wish them all the best.
"I scored a few goals there and had a good tally of six up until February. I was gutted to miss the last two or three months of the season just gone.
"I was really enjoying my football and would like to wish Hull all the best."
Hunt joined Hull last summer from Reading for an undisclosed fee and made 27 appearances, scoring six goals, before his season was cut short in February by a foot injury.