He will join the club under new coach Dave Rennie for the 2017/18 season, subject to a visa and medical.
Kebble, 24, is a former South Africa under-20 international, helping the junior Boks win the 2012 World Championship.
He could become eligible to represent Scotland in three years’ time under residency rules.
The 6ft 3in front-row forward has signed a two-year-deal at Scotstoun and will arrive following his commitments with the Stormers and Western Province.
The son of former Springbok Guy Kebble, he has made 34 appearances for the Stormers.
He is a close friend and flat-mate of Scotland centre Huw Jones who has also agreed to leave Stormers to join the Warriors in the close season.
Kebble told glasgowwarriors.org: “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 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.”
Outgoing Glasgow Warriors 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.”