The game will be live on BT Sport.
The new tournament features the top teams from across Europe and along with Aviva Premiership side Bath, the Warriors have been drawn with Montpellier and Toulouse from the Top 14 in France.
In Round 2 Gregor Townsend’s squad will face Montpellier at the Stade Yves-du-Manoir on Saturday 25 October (ko 6.15pm) live on Sky Sports, before a double header with Toulouse in December.
The Warriors will be away to Toulouse first on the weekend of 5/6/7 December and will then host the Top 14 side the following weekend, ahead of crucial GUINNESS PRO12 games against Munster and Edinburgh at Scotstoun that month.
In Round 5 the Warriors will face Montpellier at Scotstoun on the weekend of 16/17/18 January and their final pool game will be against Bath at The Recreation Ground the following weekend.
The exact dates and kick-off times for Rounds 3-6 have still to be confirmed.
Glasgow Warriors 2014/15 Champions Cup Fixtures
Saturday 18 October - Glasgow Warriors v Bath Rugby (3.15pm) - live on BT Sport
Saturday 25 October - Montpellier v Glasgow Warriors (6.15pm) - live on Sky Sports
5/6/7 December - Toulouse v Glasgow Warriors
12/13/14 December - Glasgow Warriors v Toulouse
16/17/18 January - Glasgow Warriors v Montpellier
23/24/25 January - Bath Rugby v Glasgow Warriors