Wins for Exeter, against Ospreys, and Bordeaux-Begles, who stunned Clermont Auvergne, saw Jim Mallinder’s men qualify as the eighth-ranked side.
And that means they will have to travel to Saracens, who were the top seeds after winning all six of their pool games.
Allianz Park is not big enough to host a quarter-final, but there are suggestions that Saracens may look to install extra seats to meet the requirements.
If that does not happen, Sarries will have to switch the game, which will be played on the weekend of April 8-10, to Wembley or another suitable venue.
The winners of that match will then face either Wasps or Exeter in the semi-finals, guaranteeing that there will be an English side in this season’s Lyon final.
Leicester Tigers host Stade Francais in the quarter-finals, with Racing 92’s match at home to reigning champions Toulon completing the last-eight line-up.
Saints sealed their place thanks to Saturday’s bonus-point 22-10 success at Scarlets, with Harry Mallinder, George Pisi, Sam Dickinson and George North all on the scoresheet.
Mallinder’s men finished as runners up to Racing 92 in Pool 3.
Champions Cup quarter-final line-up (all to be played on the weekend of April 8-10)
QF1 - Saracens v Saints
QF2 - Wasps v Exeter
QF3 - Leicester v Stade Francais
QF4 - Racing-92 v Toulon
Semi-finals (April 22-24)
Winner QF1 v Winner QF2
Winner QF3 v Winner QF4