The 26-year-old - capped 14 times by the Wallabies - joins the club following seven seasons with Super Rugby side the Waratahs, scoring eight tries in 44 appearances for the New South Wales outfit to date.
Renowned for his dynamism with ball in hand, the former North Harbour Rays man helped his team to Super Rugby semi-finals in 2015 and 2018, playing a key role as the 'Tahs claimed the Australian conference title on both occasions.
He was also a vital component in helping Gordon to the 2020 Shute Shield, producing a barnstorming display in the Grand Final against Eastwood to help his team to a first title in 22 years.
Long earmarked as a potential star of Australian rugby, Dempsey's talent has seen him represent his country at every age grade level, including helping the Junior Wallabies to a fifth-place finish at the 2014 World Rugby U20 Championship in New Zealand.
He made his senior international debut against Italy in June 2017, coming off the bench in a 40-27 victory at Suncorp Stadium in Brisbane.
Comfortable across the back-row, enjoyed an illustrious start to his Wallabies career, becoming one of only a few players to be undefeated in each of his first six international appearances.
His 2019 Super Rugby form saw him selected for the 2019 Rugby World Cup in Japan by then-Australia Head Coach Michael Cheika, with Dempsey scoring his first international try in the pool stage match against Georgia.
Standing at 6'3" and weighing in at 17 stone, the Sydney native has also studied for a Bachelors of Sport and Exercise Management degree at the University of Technology alongside his rugby career.
Speaking to glasgowwarriors.org, the Wallabies breakaway was excited by the new opportunity awaiting him this summer.
"I'm very excited to be starting the next phase of my professional rugby career in Scotland with Glasgow Warriors for the upcoming 2021/22 season," said Dempsey.
"Departing NSW was an incredibly tough decision. It's a club I have spent my entire professional career since joining at the end of 2014. The Waratahs allowed me to develop as a rugby player on my home soil and represent my state which has meant the world to me over the past seven seasons. I leave with very fond memories of the players, coaches and fans and wish the team, coaching staff and entire organisation the best of success."
"However, the move to Glasgow presents such a different challenge both in lifestyle and rugby, and personally it feels like the right time to take that challenge head-on.
"It's a club with such a rich and long history and I'm looking forward to joining their campaign and working with Danny Wilson and the team."
On the signing on Dempsey, head coach, Danny Wilson, said: "Jack is a really exciting addition to our squad.
"For a 26-year-old he's very experienced, having made almost 50 appearances for the Waratahs and earning 14 caps for his country.
"Jack can play across the back row and is extremely dynamic, a great ball carrier and an impressive defender, who gets over in the ball and jackals well.
"We've been looking to strengthen our back-row options for next season and Jack is just the man to do that.
"We're looking forward to having him at Scotstoun next season."