Warriors confirmed Jones had signed a two-year deal, subject to a medical.
The 23-year-old started in Scotland’s opening RBS 6 Nations win over Ireland on Saturday, winning his fourth cap for his country.
The versatile Edinburgh-born back moved to South Africa after finishing school and joins from Stormers. Jones has scored five tries in 24 Super Rugby appearances for the Cape Town side. He has also played 16 times for Western Province and scored six tries in seven Currie Cup ties last year.
Jone told the Warriors’ official website: “It felt like the time was right to join Glasgow, having enjoyed my time in Cape Town playing Super Rugby. Obviously playing for Scotland, it makes a lot of sense to be playing in Scotland and I was ready to make the move.
“Glasgow are doing very well this year and look like they could continue to do well over the next couple of years and the chance to be part of a successful club was a big factor when I was making my decision.
“Playing professional rugby in the Northern Hemisphere for the first time will be a great challenge. The Guinness PRO12 looks like an exciting championship with lots of strong teams and the European Rugby Champions Cup is obviously a massive competition too and one I’m looking forward to competing in if Glasgow qualify.”
Jones will join Warriors at a time of change with Dave Rennie set to take over when Gregor Townsend moves to become Scotland head coach. But national team coach Jason O’Halloran is moving in the opposite direction.
Jones said: “I really like working with Jason as a coach, we work well together at Scotland and obviously he has worked with Dave Rennie before. I’ve never worked with Dave but he’s been really successful with the Chiefs, so I’m really looking forward to working with world-class coaches.
“I get on well with all the Glasgow boys having got to know them in Scotland camp and I spoke to them about the club and the city and they all had really good things to say.”
Townsend added: “We first made contact with Huw three years ago when he was playing Varsity Cup rugby in Cape Town and it’s been great to see how much he has developed at both Currie Cup and Super Rugby level.
“He also played very well for Scotland during the Autumn Tests and I’m sure he will fit in very well at Scotstoun next season.”