Predominantly a tighthead, he is comfortable playing either side of the front row.
McCallum, 25, has been capped three times by Scotland, his last appearance for the national side coming on the 2018 North American tour.
As has become regular practice, Glasgow have not announced the length of the contract but said McCallum would be available “for the opening section of the new United Rugby Championship and Heineken Champions Cup campaigns”.
McCallum, who played 63 matches for Edinburgh, has joined his new team-mates for their first block of pre-season training and Warriors coach Danny Wilson said he had settled in well.
“It’s great to be able to add another capped international to our already experienced depth at tighthead,” said Wilson.
“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.”
McCallum said the prospect of working with new Glasgow scrum coach Al Dickinson was part of the appeal of joining the Warriors.
“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.”
The prop added: “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.”