It will be a first RWC semi-final for both Gardner and O’Keeffe.
Gardner (Australia) will be joined at the Stade de France by assistant referees Nic Berry (Australia) and Karl Dickson (England), with Ben Whitehouse (Wales) as Television Match Official.
Assisting O’Keeffe at the same venue 24 hours later, will be assistant referees Andrew Brace (Ireland) and Paul Williams (New Zealand) and TMO Brendon Pickerill (New Zealand).
O'Keeffe will referee a Test between the Boks and England for the second time, having been in the middle for South Africa’s 42-39 victory in June 2018.
The selection is based on merit and the wider team will remain in contention for the Rugby World Cup 2023 bronze final and final.
World Rugby also confirmed that South Africa's Jaco Peyper wasn't considered, owing to a calf injury sustained during the quarter-final between Wales and Argentina in Marseille.
World Rugby High Performance 15s Match Officials Manager Joël Jutge added: “Congratulations to all selected. This is a team effort, and the selection reflects the hard work of the group as a whole, and the encouragement and support they give each other.
“I would also like to pay tribute to Jaco Peyper, who has been ruled out through injury. He would have been in contention. We wish him a speedy recovery.”