The 30-year-old joined from Newcastle Falcons in 2012 and signed a new contract last season to stay at Scotstoun for a further three years.
Tim played 120 for the Falcons and becomes only the second player in Glasgow history to play 100 times for both the Warriors and another club, the other being Dougie Hall who represented Edinburgh more than 100 times.
He starts in the second-row as part of an unchanged tight five from Rounds one and two.
Matt Fagerson is the only change in the pack from the Ospreys game, starting at blind-side flanker ahead of Ryan Wilson.
Henry Pyrgos will captain the side in Wilson's absence, starting at scrum-half with Finn Russell outside of him.
Alex Dunbar, who was Man of the Match against the Ospreys last weekend, shifts from 13 to 12 and is joined by Nick Grigg in midfield.
Tommy Seymour will make his first appearance of the season, following his summer with the British and Irish Lions, joining Lee Jones and Ruaridh Jackson in the back three.
On the bench, Nikola Matawalu is included in a matchday squad for the first time since rejoining the club.
Both George and Peter Horne are named as replacements and Alex Allan and Chris Fusaro are involved for this first time this season.
Glasgow Warriors Head Coach Dave Rennie said: "It's a great occasion for Tim (Swinson) and his family.
"To play 100 games for two clubs is a hell of an achievement and shows his durability. His physicality and competitive edge is massive within the group and it's great that he gets to join a pretty elite club.
"It's great to have Tommy (Seymour) back too. He's a really good finisher, a great communicator and is certainly very competitive. He's been working hard in training and now he gets the chance to get out and play a bit of footy back in the jersey.
"Niko has been a real handful on the training pitch since coming back. He's got a great personality and the boys love him. It's great to see him back in Glasgow colours.
"We're focused on what we need to do and where we need to improve. We ended up winning well last week but we were slow in our contact support and didn't defend individually as well as we need to, so they've been big focusses this week. If we get that right and improve those areas, we'll be in with a good shot."
14 Tommy Seymour
13 Nick Grigg
12 Alex Dunbar
11 Lee Jones
10 Finn Russell
9 Henry Pyrgos CAPTAIN
1 Jamie Bhatti
2 George Turner
3 Zander Fagerson
4 Tim Swinson
5 Scott Cummings
6 Matt Fagerson
7 Callum Gibbins
8 Adam Ashe
Substitutes
16 Pat MacArthur
17 Alex Allan
18 D'arcy Rae
19 Brian Alainu'uese
20 Chris Fusaro
21 George Horne
22 Peter Horne
23 Nikola Matawalu
Unavailable players: Fraser Brown (ankle), Jonny Gray (wrist), Adam Hastings (thigh), Stuart Hogg (shoulder), Oli Kebble (foot), Patrick Kelly (ankle), Lelia Masaga (calf), Ratu Tagive (achilles), Leonardo Sarto (groin), Richie Vernon (achilles), Samuela Vunisa (knee) and Ryan Wilson (neck)