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Livermore, 26, has a signed a two-year contract with The Tigers after seemingly failing to impress Leeds boss Kevin Blackwell during his brief stay at Elland Road.
"At the time of signing David, Kevin Nicholls and another potential midfield target weren't available to us," read an official statement from Leeds.
"We then managed to acquire Kevin Nicholls and things have now opened up on another target.
"The situation with David is that with everyone fit he is unlikely to play. He's an honest professional and when the opportunity came up for him to talk to Hull we gave him that choice.
"We wish David all the very best for the future."