The 20-year-old, currently on loan at Alloa Athletic, has committed to Pittodrie until the end of the 2013/14 season.
Low has not featured for the Dons first team this season, but he has vowed to challenge for a place when his loan deal at Alloa expires.
He said: "I'm delighted to be staying and really looking forward to fighting for a place in the squad when my loan ends at the end of this month.
"I was on loan at Forfar last season and now Alloa but the message has always been that there is a place for me at Aberdeen.
"I also feel I've developed considerably as a player during my times at Station Park and Recreation Park and hopefully the Dons will reap the benefit when I return."
Fellow Aberdeen youngsters Cammy Smith, Jamie Masson, Jordon Brown, Joe Shaughnessy and Declan McManus have all agreed extended deals in recent weeks.