The 28-year-old assumes the role ahead of his fifth season with the club, having initially moved to Scotstoun in February 2019.
He becomes the eleventh player to be handed the captaincy of Glasgow Warriors, taking over from previous co-captains Ryan Wilson and Fraser Brown.
Equally comfortable in the centres as he is on the wing, the former University of Stellenbosch student has scored 13 tries in his 49 appearances in Glasgow colours to date.
Initially catching the eye while representing Scotland 7s, Steyn made his Glasgow Warriors debut in a 38-34 victory away to Cardiff, going on to be named as McCrea Financial Services Warrior of the Month award - jointly with Stafford McDowall - at the end of his first full month at Scotstoun in March 2019.
He then played an integral role in the Warriors' run to the 2019 Guinness PRO14 Final at Celtic Park, and has since then gone from strength to strength in black and blue.
Having spent 14 months on the sidelines due to a combination of injury and the COVID-19 pandemic, an inspired performance saw Steyn score in a 29-19 win over Edinburgh in the 2021 Guinness Rainbow Cup on his return to Scotstoun.
His determination and work ethic in his recovery saw him named as the 2021 recipient of The Famous Grouse Coaches Award, putting in the hours with the analysis team to help those selected prepare in the best possible manner in addition to completing his own rehabilitation programme.
Steyn's form continued to be of a high standard in 2021/22, touching down for a brace of tries and earning Player of the Match honours in a 27-17 victory over Newcastle Falcons in the Challenge Cup round-of-16.
Capped five times by Scotland to date, he made history on his first start for his country by crossing for four tries in a 60-14 win over Tonga at BT Murrayfield, becoming the first male player since Gavin Hastings in 1995 to achieve the feat and the first to do so at the home of Scottish rugby.
"It's a massive honour for me, and something that I find incredibly humbling," Steyn told glasgowwarriors.org.
"I love this club, so when Franco asked me to take on the role of captain I was both shocked and grateful. We're going in an exciting direction as a group, and it's huge privilege for me and my family.
"Franco sat me down just before training and asked how my wedding went, first of all! He then explained his thinking, and then asked me if I'd like to be captain. Ryan [Wilson] and Fras [Fraser Brown] both came up to me as soon as they'd heard and said congratulations, and said we'd grab a beer later on. They've been great as captains and I can't thank them enough.
"Being involved off the pitch with the cultural side of things as much as I can be really helps me understand the gravity of this club and what it means to everyone associated with it. I'm excited to take that mantle on.
"First and foremost, we want to be a team that plays in a style that reflects the city that we represent. We want to be inspired by our city and to fight for everything like our city and the people that live here have done throughout history.
"On the field, the goal is to win the URC. That might sound ridiculous to some, but that's the kind of tone that we need. We know it's not going to be an easy road to get there, but I truly believe that this group of players is capable of doing something special."
Head Coach Smith added: "Kyle represents everything that Glasgow Warriors stands for. On and off the field, he understands and embodies our club's values. He leads by example, and he's part of a new generation of Warriors that can take this club forward.
"As well as that, though, he's just an absolutely stand-up guy. The way he goes about his business is that of a model professional, and the full squad respects him to a man.
"Good people make good players is one of my biggest philosophies as a coach, and leading off the field is equally as important as leading on the field. We only represent this club for a short while, and we must leave something as a legacy for the generations to follow.
"We firmly believe that Kyle is someone who can help us leave a footprint for those to follow."