The 25-year-old has played in six HSBC World Rugby Sevens Series tournaments for Scotland having been named a core squad member at the beginning of the season.
A former student at the University of Stellenbosch, South African-born Steyn has played 15s rugby in the Currie Cup for the Griquas and was named as the side's captain for their 2018 campaign.
Steyn will remain a core Scotland 7s player for the remainder of the current season, but will join up with Glasgow Warriors when not playing on the 7s circuit.
Speaking to glasgowwarriors.org, Steyn 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 7s, 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 and I'm sure I'll learn a lot from all the players and coaches."
Glasgow 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 7s circuit for Scotland and in the Currie Cup for the Girquas before that.
"He comes highly recommended from John Dalziel and we're pleased to continue our recruitment ahead of next season."
Scotland 7s Head Coach John Dalziel said: "Kyle is a fantastic athlete, 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 7s programme both on and off the field and I'm excited to see how he can develop further playing 15s at such an established club like Glasgow Warriors, where he will work with some great players and coaches."