Saracens ensured England will have a side in the Heineken Cup quarter-finals while Edinburgh reached the last eight for the first time in eight years.
Sarries' 26-20 win against Treviso saw them top Pool Five, while Edinburgh's bonus-point win over London Irish saw them top Pool Two from Cardiff Blues.
Saracens will host Clermont, Edinburgh welcome Toulouse, the Blues travel to Leinster and Munster host Ulster.
"It is going to be a massive challenge for us," said Sarries hooker John Smit.
The former South Africa captain, who spent a season at French side Clermont earlier in his career, added: "Clermont are a fantastic club with quality players throughout the squad.
"I know from my time there that they always want to do well in the Heineken Cup. But at Saracens, we are looking to create our own legacy with the squad of players we have."
Edinburgh's achievement is doubly significant because they are the first Scottish team to book a home Heineken quarter-final since the tournament began more than 16 years ago.
"This is a huge step forward for Edinburgh rugby, first and foremost, and to the players here who made a commitment to each other in September of this season when we set out some objectives and how we wanted to play the game," said coach Michael Bradley.
"We made a commitment to areas we haven't been good at in the past, and we have had some brilliant games here at Murrayfield against Racing Metro and Cardiff Blues.
"The boys have achieved what they set out to do so far, and it's great for Edinburgh rugby."
In the semi-finals Saracens or Clermont will host the winner of Leinster v Cardiff Blues, while in the other semi Munster or Ulster will be at home to the winner of the Edinburgh v Toulouse quarter-final.
Meanwhile, in the second-tier European Challenge Cup quarter-finals Wasps will host Biarritz, Exeter travel to meet Stade Francais, Brive host the Scarlets and Toulon entertain Premiership leaders Harlequins. The ties will be played on 27-29 April.
In the semi-finals, Toulouse or Quins will meet Stade or Exeter, with Wasps or Biarritz facing Brive or Scarlets.