Furthermore, Wayne Barnes is set to take charge of a record fourth match at this stage.
Peyper will referee the first quarter-final between Wales and Argentina at Stade de Marseille in Marseille on Saturday, 14 October (17h00), with South Africa's Marius Jonker named TMO for this clash.
Barnes (England) will then referee Ireland v New Zealand at Stade de France in Paris on the same day (21h00).
On Sunday, Mathieu Raynal (France) will take charge of the third quarter-final between England and Fiji at the Stade de Marseille in Marseille on 15 October (17h00).
O’Keeffe (New Zealand) will referee the final quarter-final, between the Boks and France, at the Stade de France on Sunday (21h00).
The wider match official group remains in contention for future appointments at the tournament.
Match official appointments:
Quarter-final 1: Wales v Argentina
Stade de Marseille, Marseille
Saturday, 14 October
Referee: Jaco Peyper (SARU)
Assistant Referee 1: Karl Dickson (RFU)
Assistant Referee 2: Andrea Piardi (FIR)
TMO: Marius Jonker (SARU)
Quarter-final 2: Ireland v New Zealand
Stade de France, Paris
Saturday, 14 October
Referee: Wayne Barnes (RFU)
Assistant Referee 1: Matthew Carley (RFU)
Assistant Referee 2: Christophe Ridley (RFU)
TMO: Tom Foley (RFU)
Quarter-final 3: England v Fiji
Stade de Marseille, Marseille
Sunday, 15 October
Referee: Mathieu Raynal (FFR)
Assistant Referee 1: Nic Berry (RA)
Assistant Referee 2: Pierre Brousset (FFR)
TMO: Ben Whitehouse (WRU)
Quarter-final 4: France v South Africa
Stade de France, Paris
Sunday, 15 October
Referee: Ben O'Keeffe (NZR)
Assistant Referee 1: Paul Williams (NZR)
Assistant Referee 2: James Doleman (NZR)
TMO: Brendon Pickerill (NZR)