The 27-year-old second-rower will make the move north at the conclusion of the current season, joining a second-row stable that includes fellow Scotland stars such as Scott Cummings, Max Williamson and Alex Samuel as preparations continue for the new campaign.
Born in Dumfries, Craig was a key member of the Scotland U20 squad that achieved a fifth-place finish in the 2017 World Rugby U20 Championship, lining up alongside future Glasgow and Scotland team-mates such as Matt Fagerson and Stafford McDowall.
After impressing for Hartpury University, he then signed his first professional contract with Gloucester in February 2019, going on to make 49 appearances across a four-and-a-half year-long association with the Kingsholm outfit.
Craig made the switch to the Scarlets prior to the 2023/24 season, making an immediate impact in west Wales; his first season at Parc y Scarlets saw the second-rower make the fourth-most tackles of any player in the BKT URC, as well as ranking inside the top 10 for lineout steals across the competition.
His performances in his first season in Llanelli saw him voted as the club's Players' Player of the Season, his team-mates recognising the calibre of his displays across the campaign.
He has made 40 appearances for the Welsh outfit to date, including running out against the Warriors at Scotstoun earlier this season.
Craig has also earned six caps for his country since making his senior international debut against Italy in the 2021 Guinness Six Nations, the most recent of which saw him come off the bench in victory over Australia at Scottish Gas Murrayfield last November.
"For me, coming back home is a massive opportunity and I'm looking forward to getting stuck in," Craig told glasgowwarriors.org.
"I'm from Castle Douglas, and I've always kept a close eye on how Glasgow were doing as I supported the club when growing up. To see the club go from strength to strength in recent seasons has been so impressive, and they just keep getting better and better as a team.
"I know quite a lot of the boys from U20s and from Scotland duty; I grew up playing minis with Stafford [McDowall] too, his dad was my first rugby coach and we played together from when we were seven until about 14 or 15. Stafford's probably the one I spoke to the most when making the decision to move up here, but everyone I've spoken to has had nothing but good things to say about the club.
"I like to get myself involved in the game as much as I can, whether that's with ball in hand or being physical in defence. I just want to put my best foot forward, work hard and earn the respect of my team-mates and coaches first and foremost - it's going to be exciting and I'm looking forward to getting started."
Head Coach Franco Smith welcomed the signing, adding: "Alex is someone who we've been keeping an eye on for a while, consistently impressing with his performances for the Scarlets over the last couple of seasons.
"He is a dynamic carrier with ball in hand, whilst his statistics underline his physicality and willingness to work hard in defence.
"We know that to be a competitive team across both the BKT URC and Investec Champions Cup that we first must have a competitive squad, and we look forward to welcoming Alex to Scotstoun this summer."