The Scotstoun club are one of eight teams from the Guinness Pro14 who will play in the elite European club competition.
Glasgow finished fourth in Conference A of the Pro14 and qualify as the lowest ranked of the eight.
The 24-club Champions Cup will also feature eight teams each from the Gallagher Premiership and French TOP 14.
There will be four pool stage rounds played on the weekends of December 10/11/12 and 17/18/19 and January 14/15/16 and 21/22/23.
The knockout stages will start on April 8/9/10 with a round of 16 which will be played over two legs (second leg on April 15/16/17). There will then be one-legged quarter-finals (May 6/7/8) and semi-finals (May 13/14/15), with the final in Marseille on May 28.
Edinburgh will play in the European Challenge Cup after finishing fifth in Conference B of the Pro14.
South African teams will join the Champions Cup from the 2022-23 season.