The Blades had submitted an offer, believed to be in the region of £150,000 to £200,000 for the 29-year-old, whose deal at Valley Parade ends this summer - and his move is expected to be completed shortly.
Hanson was withdrawn from the City squad for the weekend game with Millwall ahead of his prospective move to South Yorkshire.
A Bradford club statement said: “The club would like to place on record their thanks for the wonderful and lengthy service James has given Bradford City, including some memorable goals and moments that will live long in the memory of every City fan.
“Despite James being part of our future plans, we had to make the difficult decision to let him go and respect his personal reasons for leaving.
“At Bradford City we don’t take any decision lightly. Only, after considering all the information available to us do we act and only with the best future interests of the club at heart.
“We wish James well in the future as we now focus on strengthening our squad for the rest of the season and beyond.”