Wasps got the better of Leinster at the quarter-final stage and the province also have a long-running European history with Edinburgh.
Incredibly, this is the third successive year that the Magners League rivals have been pitted against each other in the European pool.
French outfit Castres are new opponents for Michael Cheika's squad to contend with, and speaking after Tuesday's Heineken Cup pool draw, Leinster Chief Executive Mick Dawson agreed that the pool set-up presents a number of challenges.
"It's a tough draw, but there are a lot of good teams in this tournament. We bought into the new system, so we will just go ahead and deal with what we've got," Dawson said.
"They have won it twice and beat us convincingly in the quarter-finals in 2007 on their way to winning the title again at Twickenham. The real challenge, though, is going to be getting out of this pool."
Dawson also confirmed that the Leinster squad list is almost complete for next season, with one more player, rumoured to be Australia flanker Rocky Elsom, set to sign for the province in the coming weeks.
"We have about 34 guys, everything is signed, sealed and delivered but we're not confirming anything yet.
"We have one to go and hopefully in the middle of next week we'll be able to confirm the squad."