The Scotland international hooker joined the club, from Edinburgh Rugby, in January 2018 having been on loan from the capital side from September 2017. His debut came that year in Glasgow Warriors' Guinness PRO14 season opener, an 18-12 victory away to Connacht.
Since 2017 he has made 46 appearances for the club and scored nine tries. He has nine international caps and five tries for Scotland and was part of Gregor Townsend's 2019 World Cup squad.
Welcoming his contract extension, he said: "I have been at the club for three years now and I'm really enjoying it. I'm delighted to be extending my stay for another couple of years and I'm fortunate to be part of such a great club.
"The squad, the facilities, and coaches are great, and we play a really enjoyable brand of rugby where you can express yourself and try things. This is a great environment to be a part of and it has really helped my development.
"Over the next few years I am looking to push what I can do as far as possible. The last few years have been cut short for me, with various injuries and this season due to the coronavirus pandemic. I don't think I have reached my best rugby yet and I can't wait to get back on the pitch to show what I can do."
Turner re-signing with the club was secured by Head Coach Danny Wilson prior to the lockdown coming into effect in March. He follows the re-signings of scrum-half Ali Price, centres Nick Grigg and Peter Horne, winger Ratu Tagive, back-row players Robert Harley and current co-captain Ryan Wilson, and fellow hooker Grant Stewart, in committing their futures to the club since January 2020.
Wilson has also brought in Scotland and British & Irish Lions second row Richie Gray, from Tolouse, and Argentina international prop Enrique Pieretto from Exeter Chiefs over the same period.
"Knowing George from my time with Scotland I've watched him progress to become an established international hooker," said Wilson. "He is a really exciting and dynamic player with an attacking prowess. Equally, in defence he is extremely physical and provides plenty of big collisions.
"I'm thrilled George has committed his future to the club. I enjoyed working with him at Scotland and I look forward to, along with the other coaches, to bring the best out in him."
On working with Danny Wilson, Turner said: "I've known Danny for a while and we spoke a few times before I signed. We were both keen for me to stay. He can see me involved with his plans in the coming years and I look forward to working with him."