Reading have been chasing Moore for most of the summer, but Leicester turned down two bids from the Championship club and even offered the centre-back a new deal even though he has banished from the first team.
The 23-year-old had not been given a squad number or even a first-team locker in the dressing room ahead of the 2016-17 Premier League season.
Moore has struggled for first-team football at Leicester during the last two seasons and he is keen on a move away in search of regular action.
Moore is the final year of his contract at Leicester and he was prepared to run down his contract if the club did not sell him.
However, Reading have come back with a new improved bid and Leicester have reluctantly agreed to let the homegrown defender move on.
Reading manager Jaap Stam
New Reading boss Jaap Stam is keen to bolster his defensive options before the close of the transfer window and he sees former England Under-21 international as a key addition to his plans.
Moore is expected to undergo a medical at Reading before finalising his move to the Championship club in the next 24 hours.