Gibbins arrived from the Hurricanes this summer and has quickly cemented himself as a fans favourite in Glasgow. He will lead a side that sees eleven players involved in Autumn International squads recalled.
George Horne is rewarded for his man of the match performance against the Southern Kings, retaining the number nine shirt and will start alongside his brother Pete in a Glasgow jersey for the first time.
Nick Grigg and Ruaridh Jackson both return from a week at Oriam to slot into the starting line-up. Sam Johnson joins Grigg in the centre while Lelia Masaga and Nikola Matawalu start on the wings.
Jamie Bhatti, George Turner and Scott Cummings could all be in line to make their Scotland debuts this Autumn, they all pack down in the tight five and are joined by D'arcy Rae and Tim Swinson.
Robert Harley joins captain Gibbins in the back-row while Matt Fagerson will steer the back of the scrum.
On the bench Alex Dunbar returns from an injury he sustained against Cardiff Blues in September. Henry Pyrgos and Leonardo Sarto are the other returning internationals involved.
Glasgow Warriors Head Coach Dave Rennie said: "It's been a different week, we've had 19 guys in camp with Scotland but we've just got on with things.
"Tactically things aren't going to change from the last time we played Leinster we just need to do things better.
"Cully (Callum Gibbins) has been here all week helping the team prepare which made making him captain a pretty simple decision.
"He's a good man, he's earned the respect of his teammates through the way he plays and contributes an awful lot to this club. He was the obvious choice to be captain tomorrow night."
14 Lelia Masaga
13 Nick Grigg
12 Sam Johnson
11 Nikola Matawalu
10 Peter Horne
9 George Horne
1 Jamie Bhatti
2 George Turner
3 D'arcy Rae
4 Tim Swinson
5 Scott Cummings
6 Robert Harley
7 Callum Gibbins (Captain)
8 Matt Fagerson
Substitutes
16 Pat MacArthur
17 Alex Allan
18 Adam Nicol
19 Lewis Wynne
20 Matt Smith
21 Henry Pyrgos
22 Alex Dunbar
23 Leonardo Sarto
Unavailable players: Adam Ashe (ankle), Brian Alainu'uese (knee), Fraser Brown (knee), Rory Hughes (shoulder), Oli Kebble (foot), Patrick Kelly (ankle), Ratu Tagive (achilles), Richie Vernon (achilles).
Zander Fagerson (Scotland), Jonny Gray (Scotland), Stuart Hogg (Scotland), Lee Jones (Scotland), Huw Jones (Scotland), Ali Price (Scotland), Finn Russell (Scotland), Tommy Seymour (Scotland), Ryan Wilson (Scotland)