The 22-year-old loosehead has agreed a two-year contract and will move to Scotstoun in the summer.
Thornton joins second-row Andrew Davidson and winger Kyle Steyn as the confirmed new arrivals for next season.
The 6ft 3in 17st 2lb front-row forward, who has spent the past two years at the Wasps Academy, was an integral part of the Scotland U20 side which claimed a best-ever fifth-place finish at the World Rugby Under-20 Championship in Georgia in 2017.
Glasgow Warriors assistant coach Jonathan Humphreys said: “It’s great for the club and for Scottish Rugby to bring a young, talented Scottish prop back to Scotland.
“George has shown great promise in the Wasps Academy and for Scotland U20s and will add strength in depth to Glasgow’s front row next season.
“This club has a history of nurturing young, Scottish front row talent. Zander Fagerson, Jamie Bhatti and D’Arcy Rae have all become internationals whilst playing here. George is coming to an environment where he can really thrive.”
l Wales flanker Josh Navidi will be fit for Rugby World Cup preparations following successful surgery on an elbow injury.
Navidi dislocated his elbow in the Cardiff Blues’ Guinness Pro14 victory over the Scarlets on 23 March – six days after helping Wales complete a Six Nations Grand Slam.
The 28-year-old back-row forward faces a rehabilitation period of ten to 12 weeks but should be ready for the Japan-hosted 2019 Rugby World Cup, which kicks off on 20 September.