The new deal means the 21-year-old will be staying at Scotstoun until at least May 2020.
Smith is a product of the BT Sport Scottish Rugby Academy and has played 15 times for Glasgow to date, scoring two tries.
He began playing rugby at Stirling County and helped them lift the National Youth Cup in 2013.
After signing his first professional contract last January, he made his debut against the Ospreys the following month.
The flanker has played nine times for Scotland U20s and his sister Hannah is a current Scotland international playing her club rugby for Hillhead Jordanhill.
Speaking to Warriors TV, Matt said: "I'm chuffed to have signed on, I've enjoyed my time at Glasgow so far and I'm delighted to be continuing.
"The more games I've played the more I've grown in confidence.
"I've been really lucky to have the opportunity to work with some amazing players. Cully (Callum Gibbins) has been really encouraging toward me and I've learnt a lot from him.
"So far my highlight has been playing in the European Rugby Champions Cup. I loved expressing myself on the biggest stage and I can't wait for more of that over the next two years."
Glasgow Warriors Assistant Coach Jonathan Humphreys said: "We've been really impressed with Matt. He's mobile and aggressive and plays the game the way we want to play it.
"He has the potential to be outstanding and we're looking forward to watching him develop and improve over the next two years."