The 29-year-old has played in 21 sevens tournaments for the USA national team and has scored 239 points, making him the sixth highest points scorer for his country.
He joins directly from the Wellington 7s in New Zealand, where he helped the USA Eagles win the Shield on Saturday.
California-born Niua has been a regular in the USA national sevens team for the past two years, competing in the IRB Sevens World Series.
He has three caps for the full USA national team, starting against Georgia and Russia and coming off the bench against New Zealand Maori last year.
Niua, who is also a goal kicker, began his rugby career with the East Palo Alto Razorbacks, winning a Division II National Championship in 2009 and also won a Rugby Super League title with San Francisco Golden Gate.
He made his debut for the USA national sevens team at the 2011 Pan American Games and was top points scorer for the USA with 41 points, helping his country win a bronze medal.
This season he has scored the highest number of points for his country at both the Australia and USA legs of the Sevens World Series and his all action style has made him a favourite with the supporters.
Folau Niua said: "I'm really excited about this new challenge and I'm looking forward to playing in the RaboDirect PRO12 with Glasgow.
"I've played against Leone Nakarawa and Niko Matawalu on the sevens circuit and they're very good players and I enjoyed playing at Scotstoun with the USA sevens team at the Glasgow 7s last year.
"I'm looking forward to training with my new teammates. I've been playing a lot of sevens recently, so I'm fit and ready to play games.
"It'll be the first time I've played for a club in Europe, but if things go well I'd love to stay in Glasgow beyond this season. My goal is to go over there and do my best and see what happens."
Glasgow Warriors head coach Gregor Townsend said: "Folau is an exciting player who has a lot of experience, having been a regular for the USA sevens team for the past few years and now with three caps for his full national team.
"He had a cracking game against the New Zealand Maori team at the end of last year and is a real ball-playing centre who is also a very effective ball carrier.
"He is a direct replacement for Gabriel Ascarate, who left the club last week after picking up a season-ending neck injury.
"His versatility will come in useful for us in the second half of the season and we're looking forward to him joining up with us this week."