The South Africa U20 international has signed a two-year-deal at Scotstoun and will arrive following his commitments with the Stormers and Western Province.
Oli, who is the son of former Springbok Guy Kebble, has played 34 times for the Stormers to date and was a member of the South Africa U20s side that won the 2012 World Championship.
It will not be the 24-year-old's first time in the UK as he previously studied at Dulwich College in London and was part of the London Irish Academy.
The 6ft 3in prop lives with current teammate Huw Jones, who signed a two-year contract with the Warriors earlier this month.
Speaking to glasgowwarriors.org about signing, Oli Kebble said: "Glasgow is a club on the up, they are showing great ambition in Europe and are title contenders in the Guinness PRO12. It was the right club for me to go to.
"I'm really excited about playing at Scotstoun, I've heard there is a great atmosphere and I'm really looking forward to it.
"I've watched all of the Glasgow matches in the European Rugby Champions Cup this season and Northern Hemisphere rugby is getting very exciting. I'm looking forward to playing in a competitive European league.
"I know Dave Rennie is one of the best coaches in the world, so it's an exciting prospect to work under him next season.
"As a prop I pride myself on my scrummaging as well as my loose work around the park. I try and bring an edge to the game and make an impact.
"Huw (Jones) and I live together in Cape Town. We didn't really talk about it too much before it happened, but now it's nice to know there will be a familiar face in Glasgow."
Glasgow Warriors head coach Gregor Townsend added: "Oli has the physical and rugby attributes to be a dominant force in the set-piece and has a lot of experience playing in a fast-paced competition.
"He is a player Dave (Rennie) knows well from Super Rugby and his signing will help strengthen the squad for next season.”