The 32-year-old midfielder penned a short-term pay-as-you-play contract with Town last Friday and duly made his debut as a second-half substitute in the dramatic 3-2 victory at Blackpool.
Hunt, who had been without a club following his departure from Wolves in the summer, had been training with Ipswich since September, reuniting with Town boss Mick McCarthy and assistant Terry Connor having worked under the pair during their time at Molineux.
And he insists he would jump at the opportunity to stay with the Suffolk outfit longer than his current deal until January.
"I'm delighted to be here. This is a great football club and I want to do well for the lads here and the gaffer," Hunt told the club's official website.
"I'm enjoying my work and if you enjoy your work then hopefully that shows through on a Saturday.
"Hopefully I can stay here beyond January, I'd love to. The proof will be in the pudding, though. In six weeks you might be saying 'thank God we got rid of him'.
"I know what the gaffer is all about having worked with him before. If I train well and play well I'll be in the team and if I don't then I won't. It's as simple as that."