A product of Stewart's Melville College, Turner spent three years in the Scottish Rugby Elite Development Programme and three years as a professional with Edinburgh.
The most recent of his 14 Edinburgh appearances came in the 29-18 victory at Scotstoun on the last day of last season.
George, who was part of the Edinburgh squad which won the Melrose 7s in 2016, played six times for London Scottish during a short loan spell last season.
The Hooker has played 10 times for Scotland U20 and was named in Gregor Townsend's Scotland squad for the summer tour to Singapore, Australia and New Zealand.
This summer was his second experience of the national set-up having been involved in the Scotland squad for the 2016 Six Nations.
Speaking to Warriors TV, George said: "It's exciting to join the Warriors, as this is my first move as a professional rugby player.
"I know the players who were on the Scotland tour and I know a couple of players who were at Edinburgh before and are now here, as well as some younger boys from age-grade rugby, so it has been an easy transition and easy getting started.
"Fraser Brown has been in the form of his life, he's been playing really well. I've seen him develop over the last few years after he came here (from Edinburgh) and hopefully I can do the same and push on from where I am now.
"James (Malcolm) and Pat (MacArthur) are two great players and with Fraser out injured it gives me a bit of a chance, so hopefully I can impress in pre-season and make my mark in the team.
"Dave Rennie is the Chiefs coach and they play the quickest rugby in the world and he'll probably bring that here and Glasgow play quick rugby already. So it's going to be fast-paced rugby and a lot of skill will be needed to keep up with that pace.
"Jonathan Humphreys was really keen to get me on board and I spoke to him when he was a Scotland coach and around Edinburgh, so I know what he's looking for me to bring here, so hopefully I can deliver."
Glasgow Warriors Assistant Coach Jonathan Humphreys added: "George is a capable and hungry player who we believe will add to the competitiveness of our squad.
"He will have learnt a lot from his time away with the national side and has made a good impression in his first few days of training here at Scotstoun."