The 26-year-old, capped 14 times by the Wallabies, will move to Scotstoun for the start of the 2021-22 season.
Dempsey, who played at the 2019 Rugby World Cup, has spent the past seven seasons in New South Wales with Super Rugby side the Waratahs, helping them win the Australian conference in 2015 and 2018.
The 6ft 3in 17-stone player is comfortable playing across the back row.
“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,” Dempsey told glasgowwarriors.org.
“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.”
Glasgow coach, Danny Wilson, said: “Jack is a really exciting addition to our squad. At 26 years 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.”
Edinburgh also completed a smart piece of business, tying down local boy Jack Blain on an extended contract.
The 20-year-old, who can play wing or full-back, impressed in the early part of the season and is seen as a player of real promise.
Edinburgh coach Richard Cockerill said: “Hopefully, with the right application and commitment, he’ll continue to grow into being a prominent part of Edinburgh’s back-three in the years to come.”