The Chiefs were rewarded for their entrance into Europe's premier club competition with a formidable pool that also includes Clermont Auvergne and Scarlets.
But it is the meetings with Leinster, who have won the tournament in three of the last four years and are targeting a third successive crown, that really excites head coach Rob Baxter.
"It's kind of what we wanted and it's kind of what we anticipated," Baxter said.
"As one of the bottom seeds in the competition we always knew we would probably get drawn into a tough group.
"It doesn't come any tougher than Leinster, Clermont and Scarlets.
"They are three well-established Heineken Cup sides, but this is the way to do it.
"Playing Leinster is obviously fantastic for the club, our players and the supporters."
While Exeter could have asked for few more challenging opponents, English champions Harlequins have been gifted a kind draw.
Biarritz will provide the stiffest opposition of Pool Three, which is also made up of Ireland's weakest province Connacht and Italian side Zebre, who have replaced Aironi Rugby in the RaboDirect PRO12.
Quins failed to qualify for the quarter-finals last season and their England lock George Robson wants the club to make their presence felt in Europe.
"You have got to respect any teams you play against. We are more than aware that if you are not right on any given day, you are going to be in trouble," he said.
"We are more than aware how close we came to the quarter-finals last time.
"We are happy with the year we had but we have got to make sure we keep pushing domestically and in Europe as well.
"We want to play in the big games and test ourselves against the best.
"As far as the best goes in club rugby, you are looking at the Heineken Cup."
Leicester, Harlequins' victims in last month's Aviva Premiership final at Twickenham, have been matched alongside French heavyweights Toulouse in Pool Two with the Ospreys also present.
Saracens face a challenge to qualify for the knockout stages after being picked alongside last season's semi-finalists Edinburgh and two-time winners Munster in Pool One.
Northampton must contend with Ulster, who were crushed 42-14 in last season's final, in Pool Four.
A tricky Pool Six sees Sale meet Cardiff, Jonny Wilkinson's Toulon and Montpellier.
While the participation of English and French clubs in the tournament for the next two seasons are guaranteed, their ongoing involvement has been placed in doubt.
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