Barmby, who can operate at either left-back or left-midfield, has impressed for Steve Beaglehole’s side in the 2014/15 campaign, most notably scoring an injury-time winner in the 3-2 victory over his former club Manchester United in November.
Having spent time on loan at League 2 side Hartlepool United where he scored five times in 17 appearances last season, Jack is certain to gain some invaluable experience in England’s second tier.
The youngster follows in the footsteps of Foxes first-team attacker Tom Lawrence, who made six appearances for the Millers in the month he spent at the New York Stadium earlier this season.