Spencer, who also had a loan spell at Curzon Ashton, made 10 appearances for the Terriers' reserves this season, scoring one goal.
Huddersfield manager Lee Clark told the club's official website: "I recently informed Spencer that he would not be getting an extension to his contract and as I have said all along, I will do everything to help the young players that are not lucky enough to get a deal here to find a new Club.
"That is the reason I told Spencer my decision so early - I don't want him to be struggling to find a new club at the end of the season along with the thousands of other youngsters in the same position. Thankfully that has worked out for him.
"He is a magnificent young man and this is the worst part of my job - Spencer has worked very hard all season. However, I have told him that this isn't necessarily the end of his league career - he now has the chance to forge a path elsewhere, and I wish him the best of luck."