The 20-year-old, currently on loan at Alloa Athletic, will remain at Pittodrie until the summer of 2014.
He told the club's official website: "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."
Low joins Cammy Smith, Jamie Masson, Jordon Brown, Joe Shaughnessy and Declan McManus in agreeing extended deals in recent weeks.