The 25-year-old, who has played in six HSBC World Rugby Sevens Series tournaments for Scotland, will remain a core Scotland Sevens player for the rest of the current season.
South African-born Steyn will join up with the Warriors when not playing on the Sevens circuit.
Speaking to glasgowwarriors.org he said: “I’m stoked for the opportunity.
“Glasgow are a massive club and play some great rugby, so I couldn’t be happier.
“I’ve learned so much playing Sevens. It’s helped me both in attack and defence and I’m excited for the rest of the season on the circuit.
“It’ll be good to integrate with the Warriors a bit this season.
“I’ve spent some time at Scotstoun before and they’re a great bunch of boys. I’m sure I’ll learn a lot from all the players and coaches.”
Steyn has played XVs rugby in the Currie Cup for the Griquas and was named captain for their 2018 campaign.
Warriors head coach Dave Rennie said: “Kyle has come in and trained with us a couple of times before and we’ve been really impressed with him.
“He’s a big, powerful man who has performed well on the Sevens circuit for Scotland, and in the Currie Cup for the Griquas before that.
“He comes highly recommended from John Dalziel, and we’re pleased to continue our recruitment ahead of next season.”
Proclaiming Steyn “a fantastic athlete”, Scotland Sevens head coach Dalziel added: “It’s very rare to have such a big man who is fast and able to repeat those efforts over and over.
“He has really added to our Sevens programme both on and off the field, and I’m excited to see how he can develop further playing XVs at such an established club like Glasgow Warriors where he will work with some great players and coaches.”