Hunt admits Wolves' determination to bring him to Molineux helped make his decision to switch to the Black Country an easy one.
Mick McCarthy today finally ended his long-running pursuit of the Republic of the Ireland winger when he completed a move for an undisclosed fee from Hull, penning a three-year deal.
Hunt admits "two or three" rival clubs were in the running for his signature but Wolves finally got their man 12 months after first showing an interest, and for a fee believed to be considerably less than the £5million bid they saw rejected back in January.
McCarthy's admiration is made all the more clear by a foot injury - sustained against Wolves back in February - which will rule the 28-year-old out of the start of the new Premier League season, although Hunt is refusing to put a timescale on his return.
But he does stress Wolves' strong desire to secure his services contributed towards making up up his mind.
He said: "Of course it has helped. When Wolves came in, and obviously I'm not fit yet, they put so much faith in me and you think 'to be honest they really want me and I really want to go there'.
"I always wanted to come here anyway, it's job done to an extent.
"I spoke to Mick when I got permission to speak, he really wanted me so that helps but I've got competition here."
He added: "Obviously Hull are not in the Premier League any more and having spoken to the chief executive and the manager more importantly, I was convinced to come here.
"The facilities and the structure of the club is pretty good and I've got a lot of friends here so that helps."
Hunt struck an agreement with Hull chairman Adam Pearson that he would be allowed to leave should the Tigers suffer relegation from the top flight, a decision made easier for the cash-strapped East Yorkshire outfit considering he was one of their most saleable assets.
He can now look forward to linking up with former Reading team-mates Kevin Doyle and Marcus Hahnemann - with Hunt having formed a threatening double act with the former during their time together at the Madejski Stadium.
"Having Kevin Doyle and Marcus Hahnemann here - they're the two obvious ones," he said.
"But I know Andy Keogh, Kevin Foley, Stephen Ward (from international duty) and hopefully I'll get to know the rest of the players well too.
"Hopefully I can score the same amount of goals if not more if I stay injury free and set up a few goals for Doyler or whoever's playing up front, that's my job to get plenty of crosses into the box."
Hunt also hopes the switch will help boost his international career with Ireland.
And after the nation's controversial play-off defeat to France, he has little sympathy for the problems littering their World Cup campaign in South Africa.
"What comes around goes around to an extent when it comes to that," he added.
The former Brentford, Reading and Hull man is Wolves' fifth signing of the summer after Tigers team-mate Steven Mouyokolo, Jelle Van Damme, Steven Fletcher and Adlene Guedioura.
Chief executive Jez Moxey admits there no other imminent signings, although he is more than happy with the addition of a player he believes will add the key factor Wanderers were missing last term despite their superb 15th-placed finish.
"We said from the beginning of last season that we wanted to sign as much Premier League experience as we could and I think we got some criticism for not signing enough," said Moxey.
"First and foremost, Stephen brings that experience that I think we were lacking last year although we did so well.
"He's clearly a versatile player and a high-quality player so we think we've signed a star player in Stephen that can really make an impact once he's fit."