He will join on a two-year contract in October, following the conclusion of his Mitre 10 Cup commitments with the Tasman Makos.
Tipping the scales at 120kg, Siua has been a fixture in the Highlanders squad during the past season.
Having made his debut for the Dunedin-based side against the Hurricanes in 2016, the prop has since gone on to make 26 appearances in Super Rugby.
This season he helped the Highlanders reach the quarter-finals, with the side eventually losing to the Crusaders in a game which the Tongan came on as a second-half replacement.
Sila will be familiar to at least one of his new teammates, having lined up against Tommy Seymour during the Highlanders' recent 23-22 victory over the British and Irish Lions. Indeed, it was the 30-year-old's impact off the bench that helped win a crucial late penalty, from which Marty Banks kicked the winning points.
He made his debut for Tonga in 2014, appearing off the bench in a 23-9 win over Georgia. He has since gone on to win six caps for his country and featured in their famous 19-17 victory over Italy in November 2016.
Sila will be looking to leave New Zealand on a high as he seeks to help Tasman repeat their run to the 2016 Mitre 10 Cup Final, whilst adding to his 38 appearances for the Makos.
The prop also has experience of European rugby, having made 10 appearances for French side Narbonne as a medical joker in the 2014/15 season.
He becomes the 10th new player to join the club ahead of the new season, with Huw Jones, Callum Gibbins, Oli Kebble, Adam Hastings, Lelia Masaga, Samuela Vunisa, Kiran McDonald, Brandon Thomson and George Turner already signed up.
Speaking to glasgowwarriors.org, Siua said: "I'm excited to be joining Glasgow Warriors with my family later this year.
"It is a team aiming for titles and big things which excites me.
"I've heard about their loyal supporters and the great club atmosphere and I look forward to being a part of this in the near future."
Assistant Coach Jonathan Humphreys added: "Siua comes with a lot of experience, having played regularly in Super Rugby over the past two seasons.
"He will be a great addition to our squad and will add to the competition at tight-head."