The deal will see the 29-year-old provide cover for the remainder of the 2019/20 campaign, as well as the beginning of the 2020/21 season and proposed international window.
Full-back Bryce re-joined the club in the summer of 2019, having previously enjoyed a two-year stint at Scotstoun from 2014 to 2016.
The Alloa man has made 11 appearances in all competitions to date this campaign, including appearances in Glasgow's two concluding Heineken Champions Cup pool stage fixtures against Exeter and Sale Sharks.
Bryce also helped Scotland 7s to back-to-back titles at the London 7s in 2016 and 2017.
"It's really good to be able to extend my stay at the club," Bryce told glasgowwarriors.org.
"Obviously with everything that's happened with COVID-19, it's brilliant to be preparing for a game once again. I'm focused on enjoying my rugby and getting back out there - I had a good run of games earlier this season ahead of the suspension, so it's about making the most of the opportunities that come my way.
"All of the boys are champing at the bit to get back into action. We're dying to get back into matches, and I can't wait to get out on the field with the boys if I'm selected this weekend."
Glasgow Warriors Head Coach Danny Wilson welcomed the news, saying: "We're glad to be able to retain Glenn's services for the next few months, as we continue to prepare for the new season.
"With the 2020/21 campaign shaping up to be unlike any other due to the sheer number of international fixtures, having a player of Glenn's calibre available to us will provide cover in an area of the squad that we'be been looking to address.
"Glenn played well for Glasgow last season and I'm looking forward to working with him."