It means the 19-year old, who was already contracted for next season, will stay with the club until at least the completion of the 2013-2014 season.
Pepper, who came through the Jets youth system and played last season in the local state league competition, made his A-League debut in December's 4-0 loss to Wellington Phoenix.
Coach Gary van Egmond, who has played Pepper in 10 games this season, is pleased with his development.
"Jacob has played well this season and it is fantastic we are securing his future at the Jets," Van Egmond said.
"It has been pleasing to see his game develop and confidence grow with the more game time he gets."
Pepper is happy with the game time afforded to him this season and the opportunity to re-sign with his local club.
"It has been great to get a regular game this season in the A-League," Pepper said.
"I am excited to know I am here for the next two years and I thank the coaches and the club for the opportunity."