The 6ft 7in Namibian, who has 14 international caps, joined the Sharks in January following a number of impressive displays at last year's Rugby World Cup in England.
The versatile Uanivi, who can also play across the back-row, is due to arrive in Glasgow next month.
"I'm very pleased to have this opportunity to play with Glasgow Warriors next season," he said.
"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."
Uanivi 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 for the new campaign.
"We're looking forward to Tjiuee joining us next month, ahead of the new season," added head coach Gregor Townsend.
"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."
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