The Scotstoun club have been paired with Perpignan and Bath in Pool A and will face both sides home and away.
The revamped competition sees 20 clubs split into two groups of 10, with the top six in each pool advancing to the last 16 after four rounds of fixtures.
The round of 16 will be completed by four teams dropping down from the Champions Cup.
Perpignan, also known as USAP, finished second bottom of France’s Top 14 last season and had to win a relegation play-off against Pro D2 runners-up Mont-de-Marsan to preserve their top-flight status.
Bath fared worse, ending up bottom of the Gallagher Premiership but staying up because relegation has been suspended in England.
Glasgow, who are looking for a new head coach following the departure of Danny Wilson, reached the quarter-finals of the Challenge Cup last season after dropping out of the Champions Cup. They lost to eventual winners, Lyon, in the last eight.
The Warriors have never played a competitive fixture against Perpignan who have the former Glasgow prop Siua Halanukonuka in their ranks.
They are more familiar with Bath, having faced them on eight previous occasions in Europe, most memorably at Firhill in 2011 when a Richie Gray try helped the Warriors to a 26-21 win, and at Scotstoun in 2014 when the home side triumphed 37-10.
Edinburgh hosted Bath last season in the Challenge Cup, beating them 41-19 at home in the round of 16 in a match in which Scotland internationals Josh Bayliss and former Glasgow prop D’arcy Rae both featured. A third Scotland cap, Cam Redpath, missed the game through injury.
Glasgow’s Pool A fixtures will be played over four weekends in December and January, with exact dates and kick-off times to be confirmed.
South African sides will be included in the Challenge Cup for the first time this season, with the Lions entering from the United Rugby Championship and the former Pro14 club Cheetahs also being invited to take part.