The new deal that will see him remain at Scotstoun until at least the summer of 2022.
The 28-year-old's decision sees him become the thirteenth player to sign up for more at Scotstoun, as incoming head coach Danny Wilson continues his preparations for the 2020/21 campaign.
Having made his debut for the Warriors back in February 2017, the winger has enjoyed a breakthrough season in 2019/20.
Tries in successive matches against the Southern Kings and Zebre saw Tagive start both of Glasgow's opening two Heineken Champions Cup matches, part of a tally of six appearances to date this season.
The Australian-born flyer's form saw him rewarded with a first-ever call-up to the senior Scotland squad ahead of the 2020 Guinness Six Nations, one of three uncapped Warriors named in Gregor Townsend's playing group.
"It was a really easy decision for me," Tagive told glasgowwarriors.org.
"I don't think I could have imagined going anywhere else to be honest. I saw Leone (Nakarawa's) interview when he re-signed in January, and he said he made the choice to come back here because Glasgow was the first club to invest in him and give him a shot. I feel the exact same way - the Warriors gave me my initial crack, and to be able to pay that back and stay on makes me incredibly happy.
"It's been an amazing year on the field for me. I couldn't ask for much more - to get my Heineken Champions Cup debut and then my first international call-up has been incredible. More than anything, though, it's been exciting to get out there and be able to show what I can bring to the team.
"I can't thank the fans enough for their support so far this season, and I'm looking forward to getting back out in front of them when everything gets back to normal. Stay safe, and we'll see you soon."
Wilson also expressed his delight at securing the services of the 6'3" winger for a further two seasons, highlighting his growth as a player over the past three years.
"Ratu's development has been clear for all to see since he arrived at Scotstoun," he said.
"He's flourished as part of the Glasgow environment, and he's established himself firmly within the squad.
"His form and desire to work hard for his team-mates was recognised with his international call-up in January, and I'm really pleased that he's committed his future to the Warriors. I'm really looking forward to working with him."