The towering centre-back, 21, attracted offers from Wolves earlier in the summer but United stood firm before 'reluctantly' accepting the approach from Hull.
United managing director Mal Brannigan, told the club's official website: "We made it clear that we wanted Harry to stay by offering him a new contract at the end of last season, unfortunately he and his representatives chose a different path.
"However, as he is under contract at Bramall Lane, we exercised our right to set our own valuation of him and after numerous bids which did not meet our expectations, Hull City increased their offer and we have reluctantly accepted.
"As we have previously stated, Sheffield United are not under pressure to sell our players but on this occasion it was deemed the best for all parties and now we move on with the aim of assisting Nigel Clough to strengthen his squad."
The change of heart appeared to be news to Hull City who had switched their attentions to other targets after having their 'final offer' for Maguire rejected by United last week.
But following Sheffield United's statement, the club's board met with manager Steve Bruce on Monday afternoon and decided to pursue the transfer once again with Maguire then undergoing a medical with the Tigers.
Maguire is now expected to complete the move on Tuesday and become City's fourth major summer signing after Bruce splashed out on Robert Snodgrass and Jake Livermore and snapped up Tom Ince on a free transfer.