The match against Mark McCall's side will be played on Sunday 14 October (ko 3.15pm).
Sevens days later Glasgow travel to face Cardiff Blues at the Arms Park. The game on Sunday 21 October will also kick-off at 3.15pm.
The Warriors will face Lyon in the back-to-back games in December, with Dave Rennie's squad travelling to France for the first match on Saturday 15 December, before hosting the Top 14 side at Scotstoun on Saturday 15 December (ko 1.00pm).
Glasgow's penultimate Pool 3 match is at home to Cardiff Blues on Sunday 13 January (ko 3.15pm), before a trip to Allianz Park to face Saracens on Saturday 20 January (ko 1.00pm) to conclude the pool stages.
All of Glasgow's games in this season's Heineken Champions Cup will be shown live on BT Sport.
Heineken Champions Cup Fixtures
Glasgow Warriors v Saracens - Sunday 14 October (kick-off 3.15pm)
Cardiff Blues v Glasgow Warriors - Sunday 21 October (ko 3.15pm)
Lyon v Glasgow Warriors - Saturday 8 December (ko 2.00pm)
Glasgow Warriors v Lyon - Saturday 15 December (ko 1.00pm)
Glasgow Warriors v Cardiff Blues - Sunday 13 January (ko 3.15pm)
Saracens v Glasgow Warriors - Saturday 19 January (ko 1.00pm)