To date Bryce has made 32 appearances across two spells at the club, having originally made his debut against the Scarlets in November 2014.
The 29-year-old Alloa native crossed for seven tries in a Glasgow jersey, most recently in November's clash with Munster at Scotstoun.
Bryce - along with brother Kevin - was a key component in the club's 2015 title-winning campaign, crossing for a vital score away to Leinster.
"Being a part of this club has been one of the proudest parts of my career,"Bryce told glasgowwarriors.org.
"Coming into the squad back in 2014 - I'm not sure I can actually explain that feeling. Getting that first game for Glasgow alongside my brother is a moment I'll never forget, and being a part of the title-winning squad in 2015 and being on that open-top bus into George Square was an unbelievable feeling.
"Every opportunity you get to wear that jersey makes it extra special, because there's so much competition for places. The fans are incredible - every time you run out at Scotstoun in front of them you feel them backing you. It doesn't matter who we were playing or what the scenario is, they're behind you every step of the way. I'm gutted not to be able to say goodbye to them properly.
"I hope that everyone saw how much it meant to me whenever I pulled on a Warriors jersey and they saw that I always tried to give my everything when out on the pitch.
"Glasgow is one of the most special clubs there is - it's a hell of a club."