The 21-year old has spent the last four months playing in New Zealand under the John Macphail scholarship, during which time he earned his first Scotland cap after being brought into the squad to face South Africa at the end of June.
The No.8 has been tied to the Warriors for the last two years and is now looking to develop more into a senior squad player by building on the two appearances he has made for the club thus far.
“It’s been a whirlwind few months for me and I’m delighted to become a full professional with the Warriors,” said Ashe.
“Playing club rugby in New Zealand and going over to South Africa to represent my country are two experiences I’ll never forget.
“Now I’ve got my first professional contract I want to continue to work hard and hopefully I’ll get more opportunities to play for Glasgow next season.”
Warriors head coach Gregor Townsend welcomes the youngster into his squad for the forthcoming Guinness Pro 12 season, which begins in September.
“Adam is the latest player to come through the Elite Development Programme and undoubtedly has a bright future ahead of him,” said Townsend
“He is also the latest to have been awarded the Macphail Scholarship and we’ve received very positive reports about him from the coaches he’s beenworking with in New Zealand.
“Adam will add to our depth in the back-row next season and it’s great news for the club that he’s going to continue his development in Glasgow.”
Warriors development coach Mike Adamson also weighed in with a positive assessment of the player’s future in the game.
He said: “”Adam has made very good progress and has really developed over the last few years.
“He has worked extremely hard and is now prepared for the transition to professional level.
“Adam has all the attributes to learn from his first Scotland cap and go on to have a very successful career.”