The former Golden Lions captain will start at number eight, alongside Tyrone Holmes and Robert Harley.
Henry Pyrgos comes in at scrum-half for Ali Price, with Chris Cusiter set to return to action following eleven months on the sidelines with a shoulder injury, after being named amongst the substitutes.
Finlay Gillies also makes his first competitive outing for the club since December 2012, having come through unscathed playing for Glasgow Hawks last weekend.
Scott Wight continues at fly-half, with Alex Dunbar coming in at inside centre and Sean Lamont starting at outside centre.
Byron McGuigan and Tommy Seymour continue on the wings.
Tim Swinson comes in at second row and he will combine with Jonny Gray, who starts for a second consecutive match after playing the full 80 minutes against Harlequins last weekend.
After winning his first cap for Scotland in the summer, Fraser Brown has been named at hooker, with Jon Welsh and Moray Low completing the front-row.
The Warriors have 13 players on the bench, including new signings Leone Nakarawa, Jerry Yanuyanutawa, Gabriel Ascarate and Richie Vernon.
Glasgow Warriors kick-off their new RaboDirect PRO12 campaign against Cardiff Blues at Scotstoun Stadium on Friday 6 September, kick-off 7.35pm.
Glasgow Warriors head coach Gregor Townsend said: “We’re really looking forward to the challenge of facing Exeter Chiefs at their home ground tomorrow.
“They are a very well coached side, who will provide us with a tough test ahead of the new season kicking off next week.
“I’m sure this will be a very useful exercise for both teams, especially as we’re going to be facing each other in the Heineken Cup this season.
“We plan to use our whole bench and give all 28 players game time this weekend.
“We’re delighted to welcome Chris Cusiter and Finlay Gillies back into the squad. Both players have had a frustrating time with injury but have shown great dedication and professionalism in their rehabilitation. We look forward to them being involved with us once again.”
Glasgow Warriors team to face Exeter Chiefs
15 Peter Murchie, 14 Tommy Seymour, 13 Sean Lamont, 12 Alex Dunbar, 11 Byron McGuigan, 10 Scott Wight, 9 Henry Pyrgos; 1 Moray Low, 2 Fraser Brown, 3 Jon Welsh, 4 Tim Swinson, 5 Jonny Gray, 6 Robert Harley, 7 Tyrone Holmes, 8 Josh Strauss (Captain).
16 Pat MacArthur, 17 Ed Kalman, 18 Jerry Yanuyanutawa, 19 Leone Nakarawa, 20 Chris Cusiter, 21 Finn Russell, 22 Gabriel Ascarate, 23 Richie Vernon, 24 Mark Bennett, 25 James Eddie, 26 Chris Fusaro, 27 Gordon Reid, 28 Finlay Gillies.