Hunt featured 11 times for Stanley last season during a loan spell from Rotherham and moves to the Store First Stadium on a free transfer following his release by the Millers.
"I thoroughly enjoyed my time here last season and staying up was a massive achievement for the club considering the position we were in in January," said the 29-year-old after agreeing a two-year contract.
"This was always a club that I was thinking about coming back to whether Leam Richardson was the manager or James got the job. I'm thoroughly looking forward to the season ahead now.
"This is a small club but the people have got big hearts and they've got great fans and terrific staff as well as players.
"Staying up last season is up there in my career achievements purely because of the way it ended. It was absolutely fantastic to be part of it.
"For me it was all about enjoying my football. I'm 29 now, I'm not getting any younger and I just want to enjoy my football and be around my family and my daughter.
"I've known James for years so obviously that helped and from the moment he spoke to me on the phone and gave me his vision I knew that I wanted to come here and sign."