The 28-year-old joins from English Premiership side London Irish on a one-year deal and subject to a visa and medical he will join his new teammates for pre-season training later this month.
He played 21 times for London Irish last season and has 10 caps for Fiji.
Yanuyanutawa becomes the Warriors' second signing this week after the club announced a deal for South African flanker Tyrone Holmes on Tuesday.
The former Brumbies prop said: "I'm very excited about joining Glasgow and I'm looking forward to playing in the RaboDirect PRO12 and Heieneken Cup next season.
"I've spoken to Niko (Matawalu) about the move and he says it's a good club, with a great bunch of boys and a good coaching system. He's really enjoying it so I'm sure I will too.
"It was good to win the IRB Pacific Nations Cup for the first time with Fiji last month and signing for Glasgow has capped off a good year for me.
"I've always wanted to play in the Heineken Cup and I didn't get that opportunity last season with London Irish. It's the pinnacle of European Rugby, like being in Super Rugby in the southern hemisphere. To get the opportunity to play against Toulon in the Heineken Cup next season would be unreal."
Glasgow Warriors head coach Gregor Townsend said: "He is an extremely powerful and mobile prop, who will give us another option in the front row.
"Jerry played a lot of games for London Irish last season and he will provide further competition and depth to our squad."
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland