Low will join Dundee on a three-year deal when his contract with Aberdeen expires at the end of the season.
The midfielder, who has previously had loan spells with Forfar and Alloa, is the third player to agree a pre-contract with Dundee ahead of next season following the signings of Rory Loy and Daryll Meggatt.
The Aberdeen youth product worked under Dundee boss Paul Hartley during his loan spell with Alloa in the 2012/13 season.
Aberdeen boss Derek McInnes said: "The option to sign an extended contract with a fellow Premiership club was one which Nicky felt he couldn't turn down. He's at an important stage in his career. I'd like to thank him for his efforts during my time with the club."
Low has been troubled by a groin injury which has restricted him to 11 appearances in all competitions this term.