The loose head prop has represented Scotland at U20 level and will join up at Scotstoun on a two-year deal.
The 22-year-old spent two years with the Wasps Academy after his time at Bishop Burton College.
Standing at 6'3 and tipping the scales at over 110kg, he was an integral part of the Scotland U20 side that claimed a best-ever fifth-place finish at the 2017 World Rugby U20 Championship in Georgia.
Thornton has made four appearances for the senior squad during his time in Coventry.
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."