Holders Leinster will face three other former winners in Pool One of next season's Heineken Champions Cup.
The Irish Pro14 champions have been drawn against Wasps, Toulouse and Bath, with 11 titles between the four sides.
Last year's runners-up Racing 92 are in Pool Four with Scarlets, Leicester Tigers and Ulster.
Exeter Chiefs, who were beaten by Saracens in May's Premiership final, are in Pool Two, alongside French Top 14 champions Castres, Munster and Gloucester.
The competition has been renamed from the European Champions Cup, having previously been known as the Heineken Cup from 1995 to 2014.
Leinster and Toulouse are the most decorated sides in the history of the tournament, with four victories each. Wasps won in 2004 and 2007, and Bath took the 1998 title.
Meanwhile, the draw for the Challenge Cup matched 2000 Champions Cup winners Northampton with three-time finalists Clermont Auvergne - Dragons are also in their pool.
The first round of European games will take place on 12-14 October.
Heineken Champions Cup 2018-19 draw
Pool One: Leinster, Wasps, Toulouse, Bath
Pool Two: Castres, Exeter Chiefs, Munster, Gloucester
Pool Three: Saracens, Glasgow Warriors, Lyon, Cardiff Blues
Pool Four: Scarlets, Racing 92, Leicester Tigers, Ulster
Pool Five: Montpellier, Newcastle Falcons, Edinburgh, Toulon
Challenge Cup 2018-19 draw
Pool One: Northampton, Clermont Auvergne, Dragons, Timisoara Saracens
Pool Two: Pau, Ospreys, Worcester, Stade Francais
Pool Three: Sale Sharks, Connacht, Bordeaux-Begles, Perpignan
Pool Four: La Rochelle, Zebre, Bristol, Enisei-STM
Pool Five: Benetton, Harlequins, Agen, Grenoble
'Playing the champions is huge' - reaction
Bath qualified for the Heineken Champions Cup by securing sixth place in the Premiership on the final day of the season with a 63-19 thrashing of London Irish.
"Once you do the hard work, like the lads did last year, to fight their way into the Champions Cup, you want the big challenges and you want the big games," Bath coach Stuart Hooper told BBC Radio Bristol.
"So going to the champions Leinster and having the champions come back to our place is huge.
"History would suggest the best way to get through the group is to win your home games. We'll be looking to get teams to the Rec and beat them, and then get a couple of results away."
Exeter director of rugby Rob Baxter said it would be "ridiculous" for his side not to chase European success in favour of regaining the Premiership title.
"We see ourselves as a strong side and we think we can compete on multiple fronts," he said.
"We're going to be really enthusiastic about Europe. We're not going to run away from challenges."
"It's a very difficult draw, but that is what you expect when you are playing against the best 19 other teams in Europe," added Dai Young, Wasps director of rugby.
"It's exciting to be drawn with the defending champions and Toulouse, who have also won the competition several times. They will be great match-ups.
"We've also had some really good games with Bath in recent seasons, including a double-header in Europe three seasons back. They will all be tough games."