The 28-year-old had initially returned to Scotstoun in the summer, alongside a group of Scotland 7s players, but will now remain with Dave Rennie's playing group.
Having made his Glasgow debut back in 2014, Bryce has scored six tries in his 23 appearances for the club to date.
New prop Aki Seiuli arrived in Glasgow on Saturday following the conclusion of his Mitre10 Cup commitments with Otago. The New Zealander joined up with the squad at Scotstoun yesterday, ahead of Saturday's game against Zebre in Parma.
Fiji international hooker Mesu Dolokoto is expected to arrive at Scotstoun later this month, having represented his country at the Rugby World Cup in Japan.
Meanwhile, Patrick Kelly has been called up to the Scotland 7s squad for the first time ahead of the season opener in Dubai next month.
The club has also confirmed that USA back-rower Tevita Tameilau has been released to explore new opportunities.
The 29-year-old made six appearances in a Warriors shirt last season, scoring his only try for the club in February's victory away to Cardiff Blues.
Hooker Pat O'Toole has also left the club following the conclusion of his short-term contract.