Steve Bruce's men have been chasing the 21-year-old throughout the close-season, with several offers for his services having already been rejected.
However, the South Yorkshire outfit have confirmed that the Premier League club have now met Maguire's asking price and their latest bid has been "reluctantly" accepted.
"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," managing director, Mal Brannigan, said.
"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."
Hull responded with a statement of their own: "Sheffield United rejected an offer from the Club five days ago for defender Harry Maguire.
"This was the Club’s final offer and we have since entered into discussions with other transfer targets.
"In light of Sheffield United’s statement this morning the board will meet with manager Steve Bruce ... to determine whether we now wish to pursue the transfer after the South Yorkshire club's apparent U-turn.
Maguire, who has represented England at under-21 level, has become a regular at the heart of United's rearguard after breaking into the team at the end of the 2010-11 season.
He made 41 appearances in League One last season as United finished seventh, seven points adrift of the play-offs.