In the quarter-finals, holders Toulon will face Wasps, three-times champions Leinster host Bath, top seeds Racing Metro take on Saracens and Clermont Auvergne play Northampton.
The draw for the semi-finals was also made with Toulon or Wasps taking on Leinster or Bath, while Clermont or Northampton face Racing or Saracens.
Toulouse started the sixth and final round top of Pool 4 but a surprise defeat by previously winless Montpellier left them out of the picture as one of the best runners-up sides in the five pools.
Lucas Dupont touched down twice for Montpellier in the first 10 minutes of the second half after Toulouse had gone 20-9 up.
But Toby Flood's boot restored Toulouse's lead before Ben Lucas kicked the decisive penalty for the hosts.
Bath, who lost their first two games in this season's competition, won the group after a nervy 20-15 success against Glasgow Warriors.
Two penalty tries helped Bath come from behind to cling on during an enthralling finish at the Rec as Glasgow, who had led after tries from Alex Dunbar and Richie Vernon either side of halftime, pushed for another score in the dying moments.
Clermont beat Saracens 18-6 to top Pool 1 with the English Premiership side also sealing a last eight berth