The 28-year-old will join the Guinness PRO14 side in July on a deal until May 2020.
Standing at 6ft 5in and weighing 122kg, Tameilau is a dynamic, ball carrying loose-forward.
David, who is also known as Tevita, currently plays for Utah Warriors in Major League Rugby, having recently joined from French side RC Narbonne.
Tameilau has represented the USA nine times, scoring two tries and was called up to the Men's Eagles squad earlier this month for their Summer Test Series, which includes a game against Scotland next month.
He has previously played for San Francisco Rush in the American PRO Rugby competition and also had spells with Newcastle Falcons in the English Premiership and Mitre 10 Cup side Taranaki.
Speaking to glasgowwarriors.org, 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 from Greg about the club.
"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. Playing in France has helped prepare me for going to Glasgow and I'm a better player for that experience.
"I'm really excited about playing in the European Rugby Champions Cup with Glasgow Warriors 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 go to Glasgow and help the team in whatever way I can and continue to develop as a player and as a person."
Glasgow Warriors Head Coach Dave Rennie said: "Tevita is a really opposing 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."