The 19-year-old, who has been with the Dons since the age of eight, has made 46 first-team appearances and is a regular with the Scotland Under-21s.
Jack told the club's official website: "I'm really pleased to have signed the new deal with Aberdeen. This is a massive club.
"I have come right through from the youngest age group in the youth academy to the first team.
"I know I have still got a lot to learn and I feel this is the right club for me to keep learning.
"I am looking forward to continuing my development as a player under the guidance of Craig Brown and Archie Knox.
"I am enjoying playing regularly and I get on great with all the lads.
"The club is going forward now under Craig and Archie and I am looking forward to see what we can achieve over the next couple of years."
Source: Team Talk