The 34-year-old forward has arrived at the Tigers, who play in the fourth tier of the non-league pyramid, from Farsley Celtic and made 15 appearances for the Blades, helping them win the League One title in 2016/17.
Hanson also won promotion with Bradford City during his time in West Yorkshire, helping the Bantams reach the League Cup final in the same season as a League Two side.
“He is an absolute monster and is a man who will play down the middle and up top,” Tigers boss Craig Parry said.
“For me, he will be one of the more important signings that we will make, and it has taken us 18 months to find someone like him to play down the middle.
“It is well known that I like a ‘number nine’ like him and then I can build everything off that. Whether that’s another striker or the two wingers.
“He brings so many dimensions to us and allows other people to come into the game and I am excited about James joining.”
Hanson, who has also moved into coaching, is keen to use his experience to help his new Tigers teammates – as well as win more silverware to add to his promotions with United and City.
“It feels good to join,” he said. “It felt right the right time to come, and it might be the icing on the cake for me to win something at the end of my career. That is what I am aiming to do, and all the signings that we have brought in are a real sign of intent.
“As a player, you want to come and win things and just with the calibre of players [Parry] has brought in, he should be looking to win the division and we shouldn’t be afraid to say that.
“It’s not just on the pitch that I want help on but off the pitch as well and I have been told that there are some good young players coming through.
“Seeing the likes of myself and a few other new lads come through the door that have plenty of experience and Football League games under their belt, I am sure they’ll help the lads.
“Hopefully they will learn off them and the standards in training and the changing rooms will improve which will make them better players and better people.”
Hanson only scored one goal for United, but was a valuable option for Chris Wilder as he looked to get the Blades over the promotion line and into the Championship.
“I am a powerful target man and I like to score goals and use my head in the air,” Hanson added.
“I will hold the ball up and bring others into play as well. There was a huge smile on my face when [the manager] told me about the wingers coming in. I look forward to playing with the squad as a whole and the start of pre-season and working hard from day one.”