The backrower has made 66 appearances for the club since making his debut against the Ospreys in 2012.
He has scored 13 tries for the Warriors and is in Gregor Townsend's Scotland squad for the Guinness Six Nations.
Ashe, who is a product of Hillfoots and Stirling County, came through Scottish Rugby's Academy Programme, which was then known as the EDP Programme.
The 25-year-old is a former recipient of the John MacPhail Rugby Scholarship and made his Scotland debut against South Africa in 2014. He has six caps for his country.
Speaking to Glasgow Warriors Official Club Podcast, Warriors Weekly, Ashe said: "I'm absolutely delighted. I'm really pleased to be staying here for another two years.
"It was an easy decision for me, I've been here for seven years now having come through the Academy, Glasgow Warriors is my second home.
"We're a club that has a lot of ambition and wants to grow and develop and really inspire the community around us and I'm really pleased to be staying here to be a part of it."
Glasgow Warriors Head Coach Dave Rennie added: "We've been really impressed with Ashy's form this season. He's a good man and we're rapt that he's staying put for another couple of years.
"He's a great athlete, really dynamic and has all the attributes of a top back-row forward. He's still a young man and we believe that his best years are still ahead of him."