Morrison, back to full fitness following his knee injury, made a substitute appearance in the Heineken Cup against Castres at the start of December and will form part of a reshuffled back-line from last week's win away at Edinburgh.
One of four changes to the starting XV in total, he lines up alongside Alex Dunbar, who is also making his return from injury. Tommy Seymour is restored to the wing in place of Sean Maitland while Stuart Hogg retains his place at full-back, while Ruaridh Jackson starts at stand-off for the fourth game in a row, with Henry Pyrgos partnering him at half-back.
DTH van der Merwe, who became the club's leading league try-scorer with a double against Edinburgh at Scotstoun, keeps his spot on the left wing.
With back-to-back wins against Edinburgh in the bag, Warriors are looking to make it three in a row against a Treviso side who are on a winning run, having triumphed twice in their own local derby against Zebre over the festive period.
Glasgow head coach Gregor Townsend said: "It's fantastic to have Graeme and Alex back starting for the team and it gives us yet more options in the midfield to add to an already deep list of talent.
"Alex was in fine form until he suffered his injury and it will be great to see him getting back to that level of performance. Everyone knows exactly what kind of influence Graeme can have on a match and against a tough side like Treviso, it's great to have someone of his experience at inside-centre.
"The selection this week again highlights the quality available to us as coaches and the fact that even with three changes to the back-line, it's still a very strong line-up."
There are minimal changes in the pack, with the heavy-hitting back row of Rob Harley, Josh Strauss and last week's man of the match, Ryan Wilson, again reunited.
In the second row, Tim Swinson comes in for Tom Ryder to partner captain Al Kellock. Ryan Grant, Doug Hall and Moray Low, hugely impressive in the scrum against Edinburgh, will again pack down together for the tough Treviso test.