The 28-year-old has become a firm favourite with fans since his arrival in the summer of 2021, making 33 appearances for the club across all competitions to date.
Dempsey made his debut against Ulster in the opening match of the 2021/22 season and went on to be nominated for the McCrea Financial Services Player of the Season award at the end of his first campaign at Scotstoun.
Having scored his first try in Glasgow colours against Leinster in the inaugural Plaster It Purple match in support of Glasgow Children's Hospital Charity, he has since crossed the whitewash on seven occasions for the Warriors.
Only Stafford McDowall and Sione Vailanu have carried more ball in the BKT United Rugby Championship for Glasgow than Dempsey this season, the number eight also offloading on 10 occasions for Franco Smith's men.
Eligible for Scotland courtesy of his Glaswegian grandfather, Dempsey made his Scotland debut during the 2022 Autumn Nations Series, making his bow in the dark blue jersey against Australia at BT Murrayfield.
He has since won nine caps for Gregor Townsend's squad to date, most recently winning the Player of the Match award in the dramatic victory over Italy at BT Murrayfield in the final round of the 2023 Guinness Six Nations.
"I'm really pleased to finalise my future with the club," Dempsey told glasgowwarriors.org.
"Ever since I arrived, this has been a club with a massive amount of ambition and aspirations to play rugby in a particular way, as well as being successful. I've enjoyed being a part of it from minute one, especially this season - we've gone to another level this year and the competition within the squad is at an all-time high.
"It's the right place for me to play my best rugby and I'm excited to see what we can achieve next. We're moving into a crucial part of the schedule and as we move into knockout rugby, that's what we as players dream of being involved in.
"Scotstoun is an electric atmosphere on the big occasions, and I can't wait to get stuck in.'
Head Coach Smith added: "Jack's quality has been clear to see every time he pulls on a Glasgow Warriors jersey, and we're pleased that he will be remaining with the club for the next couple of seasons.
"His ball-carrying is a real asset to the way we want to play and he's passionate about playing his part for this club.
"He's a fantastic athlete and it's great to see his commitment to Glasgow day in, day out."