The 17-year-old has signed a three-year deal with the club, snubbing interest from the likes of Tottenham, Juventus and Monaco.
England U17 international Duncan is the cousin of 'Reds' legend Steven Gerrard and has been tipped for a bright future in the game.
Duncan left City last August, but the club continued to hold his registration.
Rather than effectively taking a season out of the game, the youngster trained with the Wigan Athletic first team, playing behind-closed-doors games, whilst continuing to feature for Steve Cooper's England U17 side.
Liverpool are thought to have agreed to pay City in the region of £200,000 for the youngster, who will report for pre-season for his new club on July 2.