Northampton Saints will host the Bulls in the Investec Champions Cup quarter-finals, which also feature a rematch of the past two finals.
La Rochelle, who beat Leinster in those two finals, face the Irish side again after winning away at the Stormers.
Harlequins will travel to Bordeaux and Exeter Chiefs face a difficult away trip to five-time winners Toulouse.
Leo Cullen’s Leinster have suffered agonising back-to-back final defeats against La Rochelle, but they did clinch a pool-stage victory against Ronan O’Gara’s side in the opening game of this year’s tournament.
This is the fifth time in four seasons the sides have met in the competition.
Bulls remain the only South African side left in the competition after hammering Lyon 59-19 in Pretoria, and are in the last eight for the first time.
Quins’ first knockout win in Europe’s top-tier competition in their history against Glasgow results in a daunting trip to Bordeaux Begles, who hammered Saracens 45-12 in France on Saturday.
Exeter, who reached the semi-finals last season, produced a strong second-half performance to see off fellow Premiership side Bath 21-15 at Sandy Park.
Toulouse came into the knockout stages as the number-one seeds after winning all four pool games, andscored five tries in a 31-7 win over Racing 92 on Sunday.
Quarter-final fixtures
(1) Toulouse v Exeter Chiefs (8)
(4) Bordeaux Begles v Harlequins (5)
(2) Leinster v La Rochelle (10)
(3) Northampton v Bulls (6)
Seedings in brackets
Potential semi-finals
The semi-finals could see an all-English or all-French contest, with the winner of Toulouse against Exeter facing Bordeaux Begles or Harlequins.
Toulouse, as number-one seed, will have a home semi-final if they defeat Rob Baxter’s side. Victory for Exeter and a win for Bordeaux would still mean another away tie in France for the Chiefs.
If both English sides win then Quins would host Exeter.
On the other side of the draw, if Northampton overcome Bulls they will face one of last year’s finalists in Leinster or La Rochelle.
If La Rochelle win, the Saints will have a home draw, but if Leinster win, Northampton would face a trip to Dublin in the semi-finals.
Key dates
Quarter-finals – 12/13/14 April
Semi-finals – 3/4/5 May
Final – 25 May