The 22-year-old Dewsbury-born player has found opportunities hard to come back under Neil Warnock and has made just one appearance this season, as a half-time substitute in the EFL Cup loss to Middlesbrough.
High made four appearances in the final third of last season during the club's 'Great Escape' from relegation under Warnock, with his last one coming in the draw with Blackburn Rovers on Easter Monday.
The player was originally intended to spend last season on loan at Rotherham United, but was recalled in January.
His future had been in limbo after Millers chief Matt Taylor said that the player had returned to West Yorkshire at the end of 2022.
There was a recall clause inserted in the loan, although it was not initially invoked by Huddersfield. The situation remained unresolved until he was finally recalled by Town.
High - who has spent a previous loan spell at Shrewsbury Town - played 15 times for Rotherham, with 12 appearances coming from the bench.