Tameilau, who is also known as Tevita, has been capped nine times for his country and will join Warriors on a two-year deal in July, subject to a visa and medical.
The 6ft 5in 28-year-old is currently playing for Utah Warriors in Major League Rugby, after joining from French Rugby Pro D2 side RC Narbonne.
Tameilau has also had spells playing for San Francisco Rush in the American PRO Rugby competition, Newcastle Falcons in the Aviva Premiership and Mitre 10 Cup side Taranaki.
The Californian-born loose-forward was called up the Men’s Eagles squad for next month’s Summer Test Series, and he could face a number of his Scotstoun team mates when the USA takes on Scotland at the BBVA Compass Stadium on June 16.
He is Warriors’ third signing ahead of the 2018/19 season, following the return of DTH van der Merwe in March, and George Turner’s loan from Edinburgh being made permanent at the turn of the year.
Speaking to Glasgow’s website, Tameilau said: “I’m really looking forward to joining Glasgow next season. I had a good chat with Dave [Rennie] and I feel he can take me to another level as a rugby player.
“I’m really good friends with Greg Peterson and he told me a lot of great things about the team, and the environment and what they’re trying to accomplish. I heard nothing but good things.
“It was great playing in France. It was tough rugby, but a good learning experience for me. I took a lot from being there and I’ve grown as a player as well.”
Tameilau believes his stint in France has made him a better player, and has prepared him well for life at Scostoun.
He added: “I’m really excited about playing in the European Rugby Champions Cup next season, it’s something I’ve been wanting to do since I moved to France and now I’ll have that opportunity.
“I hope to help the team in whatever way I can and continue to develop as a player and as a person.”
Rennie said: “Tevita is a really imposing figure. He’s athletic, powerful and has the ability to break the gain line.
“He’s an exciting signing and will bring a point of difference. Glasgow fans will get a chance to see what he’s capable of this summer when Scotland play the USA.”