The lock forward, who recently had a short loan spell at the Southern Kings in Port Elizabeth, has penned a contract at Scotstoun until at least May 2017.
The 6ft 7in Namibia international, who has 14 caps for his country, joined the Sharks in January following a number of impressive displays at last year's Rugby World Cup.
He scored his first try for his country against Romania in the World Rugby Nations Cup earlier this month.
Prior to joining the Sharks, the 25-year-old played 10 times for Brive in the Top 14 and European Rugby Challenge Cup.
Tjiuee, who can also play across the back-row, is due to arrive in Glasgow next month.
He is the latest player to join the Warriors ahead of the 2016/17 season, with winger Leonardo Sarto, hooker Corey Flynn and scrum-half Nemia Kenatale, joining fly-half Rory Clegg and props Djustice Sears-Duru and Jarrod Firth at Scotstoun for the new campaign.
Speaking to glasgowwarriors.org, Tjiuee said: "I'm very pleased to have this opportunity to play with Glasgow Warriors next season.
"It's a club with a rich history, who play exciting rugby and have had lots of recent success, and I will do all I can to help that continue.
"The new artificial pitch at Scotstoun will really suit my style of play and I can't wait to get started with the players and coaches.
"I'd like to thank The Sharks, and Gary Gold in particular, for allowing me the chance to pursue this exciting opportunity and I wish them well in Super Rugby."
Glasgow Warriors head coach Gregor Townsend added: "We're looking forward to Tjiuee joining us next month, ahead of the new season.
"We believe he'll fit in well in our environment and challenge for a starting place in our forward pack.
"He has excellent athleticism and put in a number of impressive performances for Namibia at last year's Rugby World Cup.
"We believe Tjiuee's strengths suit the high tempo rugby we aspire to play, but he will have to work hard every day to win a starting place up against the other second rows at the club.
"We now have a really good balance within our second-row group for next season and it will be exciting to see them build partnerships and continue to improve."