Holders and three-time winners Saracens will begin their Champions Cup defence against French giants Racing 92 in Paris on 17 November.
The day before, four-time champions Leinster face Benetton Rugby.
And last season's Challenge Cup champions Clermont host Premiership side Harlequins.
Leicester start their Challenge Cup campaign at home against French team Pau after failing to qualify for the Champions Cup.
Two-time Champions Cup winners Munster and Welsh side Ospreys join Premiership champions Saracens and Racing 92 in Pool Four and play each other in the first round.
Premiership side Bath host Irish team Ulster on the opening weekend, while four-time winners and current Top 14 champions Toulouse travel to Gloucester for the first match of the tournament on 15 November.
Elsewhere, Premiership runners-up Exeter travel to France to face La Rochelle, Glasgow welcome Sale, Northampton host Lyon and Connacht play Montpellier.
In the Challenge Cup, European rugby union's second tier, Worcester play Russian team Enisei-STM, while newly-promoted Premiership club London Irish face Welsh side Scarlets.
Fellow Premiership team Bristol take on Italians Zebre and Wasps travel to Bordeux-Begles. Pro14 side Edinburgh also face French opponents in Agen, Cardiff Blues face Italian team Calvisano and Dragons play Castres.
After six rounds, five pool winners and the three best runners-up will qualify for the Challenge Cup and Champions Cup knock-out stages. The finals take place in Marseille on 22 and 23 May.
Champions Cup Round One
Friday 15 November
Gloucester v Toulouse (19:45 GMT)
Saturday 16 November
Bath v Ulster (13:00 GMT)
Glasgow v Sale (13:00 GMT)
Leinster v Benetton (15:15 GMT)
La Rochelle v Exeter (16:15 GMT)
Ospreys v Munster (17:30 GMT)
Clermont v Harlequins (18:30 GMT)
Sunday 17 November
Northampton v Lyon (13:00 GMT)
Connacht v Montpellier (13:00 GMT)
Racing 92 v Saracens (16:15 GMT)
Challenge Cup Round One
Friday 15 November
Enisei-STM v Worcester (TBC)
Agen v Edinburgh (20:00 GMT)
Stade Francais v Brive (20:45 GMT)
Bayonne v Toulon (20:45 GMT)
Saturday 16 November
Calvisano v Cardiff Blues (14:30 GMT)
Leicester v Pau (15:00 GMT)
Bristol v Zebre (15:00 GMT)
Dragons v Castres (15:00 GMT)
Bordeaux-Begles v Wasps (21:00 GMT)
Scarlets v London Irish (20:00 GMT)