On Thursday, it was reported that the Foxes had agreed a £125,000 compensation package with Chester for Hughes, who has previously been linked with Swansea City and Crystal Palace.
Leicester have now revealed that the deal has gone through, with Hughes due to represent the club's development squad next term.
"Highly-rated defender Sam Hughes, 20, will join the Development Squad on 1 July, after agreeing a move from National League club Chester on a three-year deal," read a statement on Leicester's official website.
"The powerful centre-half was Chester's Player of the Year last season, winning a host of admirers for his mature and consistent performances at the heart of the Blues defence. He joins City following the expiration of his contract and the club would like to extend its thanks to Chester CEO Mark Maguire for his support for the player and efforts to facilitate the move."
Hughes captained his Vanarama National League side during an impressive 2016-17 campaign.