The 23-year-old has been handed the deal days after making his first appearance of the season in a run-out for Ayr as he continues his rehabilitation from a hip injury.
Ashe follows Stuart Hogg, Henry Pyrgos and Greg Peterson in committing their futures to the club in recent weeks.
Ashe, who has six Scotland caps, said: “It’s a brilliant feeling to extend my contract and stay on with the club.
“Glasgow Warriors is a fantastic environment and I’m surrounded by great players, great coaches and great fans so it was an easy decision for me to make.
“As a club it is really taking off, we’ve just had two good wins in Europe and it’s exciting to be a part of something that is moving in the right direction.”