Bunn, 21, joined Huddersfield on loan in early December, primarily as part of the development squad, and following the expiry of that deal he has returned to the club on a permanent basis.
He was an unused substitute for Mark Robins side in the defeat at Ipswich on December 7.
Robins told the club's official website: "We were pleased with what we saw of Harry and he did well in a short space of time.
"He fitted in well with the group and caught the eye in his performances for the under-21s.
"Although our first-team supporters didn't get the chance to see him, the loan period proved to be extremely worthwhile for us.
"We believe Harry can develop further and we'll work hard with him on the training ground to aid that development.
"We will now continue to monitor Harry's progress here for the rest of the season, it's a good opportunity for Harry."