The deal sees the 25-year-old join Danny Wilson's squad for the opening section of the new United Rugby Championship and Heineken Champions Cup campaigns, with McCallum already having linked up with his new team-mates for the start of the first block of pre-season at Scotstoun this week.
Comfortable on either side of the front-row, McCallum makes the switch to Scotstoun following five seasons at Edinburgh.
He made his professional debut in October 2016 in a home victory over Benetton at BT Murrayfield, before going on to make 63 appearances for the capital side.
McCallum's ability at both the set-piece and around the field have also seen him catch the eye of the national selectors, with the former Dunfermline RFC man having earned Scotland honours at both U20 and senior level.
The prop was part of a talented Scotland U20 squad that competed at the 2016 World Rugby U20 Championship in Manchester, with new team-mates Zander Fagerson, Scott Cummings and Ally Miller also part of the 28-man playing group.
He then went on to make his Scotland debut off the bench against Wales in the opening match of the 2018 Guinness Six Nations, before earning two further caps in Test matches against Canada and the USA in the summer of the same year.
A product of the FOSROC Scottish Rugby Academy, McCallum also holds a UKCC Level Two Coaching certificate for rugby.
"I'm delighted at the new challenge here at the Warriors," the prop told glasgowwarriors.org.
"It's exciting to get the chance to experience a new culture and experience a new way of playing.
"Glasgow play an exciting brand of rugby and I'm looking forward to immersing myself in the club, getting to know the boys, the coaches and fighting for a jersey amongst some very experienced players.
"In my time here I'm looking to continue to develop as a player and I'm eager to get some games under my belt and get back playing on the big stage - I've seen Scotstoun packed out and I can't wait to experience it from the pitch."
The prospect of working with incoming scrum coach Al Dickinson was another element about which McCallum expressed his excitement, adding: "I'm really looking forward to working with Al.
"He was playing at Edinburgh as I was coming up. He's done some really good things as a coach, especially at Bristol, and I'm excited to get on board and work with him.
"I think he'll do wonders here."
Glasgow Warriors Head Coach Danny Wilson welcomed McCallum to the club following the announcement, saying: "We're pleased to welcome Murray to Scotstoun. It's great to be able to add another capped international to our already experienced depth at tighthead.
"He has fitted in with the squad seamlessly since joining and we're all looking forward to seeing him compete for the number three jersey as the season progresses."