The 24-year-old has agreed a two-year-deal and will arrive following his commitments with the Stormers and Western Province in South Africa.
He is the son of former Springbok Guy Kebble and won the 2012 Under-20s World Championship with South Africa.
"I try and bring an edge to the game and make an impact," Kebble told the Pro12 club's website.
"I've watched all of the Glasgow matches in the 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."
Kebble will join current team-mate Huw Jones in Glasgow, with the Scotland centre signing a two-year contract with the Warriors earlier this month.
"Huw and I live together in Cape Town," he explained. "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."
Last week, BBC Scotland revealed Kebble's expected arrival, with the new recruit considered a project player by Scottish Rugby, who have monitored him for several years.
Glasgow Warriors have confirmed the signing of loose-head prop Oliver Kebble for next season.