Hall, 18, joined the Gladiators nearly three years ago as an academy student and signed his first contract last October.
He had a trial at Leeds followed by a two week assessment with the Blades, and terms were agreed for him to join them when the transfer window opened.
Matlock Town will receive an undisclosed compensation payment for the development time he has spent with the club.
Gladiators Chief Executive Keith Brown said he was delighted for Ashton who was joining his dream club and his very supporting family on completion of the transfer after all of the hard work he carried both on and off the pitch which now provides him with the chance in the professional game with such a great club as Sheffield United with whom we have enjoyed an excellent relationship over very many years.
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