The Dewsbury-born player, 20 - who made his first competitive start in the Terriers' final Championship game of 2020-21 at Reading - has penned fresh terms with his deal now running until the summer of 2025.
The club have retained the option of a further year's extension.
B team captain High, named as the club’s Academy Player of the Year in 2019, made his first-team debut as a substitute on the final day of the 2019-20 season at Millwall and made 17 appearances in a loan spell at Shrewsbury Town in the first half of 20-21.
Upon returning to Town, High made 13 appearances from the bench in the second half of the campaign.
Head coach Carlos Corberán explained: “This is very positive for the club. During the second half of last season, Scott showed he is a player who can help the team to compete well in the Championship.
“He follows in the footsteps of another Academy graduate, Lewis O’Brien, in terms of his hard-working mentality, and it’s very positive to work with players like this.
"This highlights the excellent work that our Academy is making with our young footballers.
“He is a player who puts high demands on himself, which is something you need to play football at the top levels. He needs to continue his development, but the minutes he played for us last season will help him as he enters 2021-22.”