Folau (ankle) and Giteau (ribs) have overcome minor injuries suffered in last weekend’s victory over England.
Coach Michael Cheika has made three changes for the crucial clash, with the winner to finish top of Pool A and secure an easier path to a potential World Cup final.
Rebels young gun Sean McMahon will replace suspended vice-captain Michael Hooper after edging out Ben McCalman, while veteran Drew Mitchell replaces Rob Horne (shoulder) on the wing.
Rob Simmons has been dropped, with Dean Mumm to start in the second row.
The inclusion of McMahon allows David Pocock to stay at number eight, setting up a mouth-watering showdown with Wales fetchers Sam Warburton and Justin Tipuric.
"Every match in this tournament has required our team to step up to another level and we'll need to do that again against an undefeated Welsh team," Cheika said.
"Every player in our squad knows the improvements required, and we still have two days to continue to make them, both individually and as a team.
"Saturday night at Twickenham is another opportunity for us to put in a solid performance and continue to build towards the next stage of the tournament."
Wallabies: 1. Scott Sio, 2. Stephen Moore (c), 3. Sekope Kepu, 4. Kane Douglas, 5. Dean Mumm, 6. Scott Fardy, 7. Sean McMahon, 8. David Pocock, 9. Will Genia, 10. Bernard Foley, 11. Drew Mitchell, 12. Matt Giteau, 13. Tevita Kuridrani (27 Tests), 14. Adam Ashley-Cooper, 15. Israel Folau.
Reserves: 16. Tatafu Polota-Nau, 17. James Slipper, 18. Greg Holmes, 19. Rob Simmons,
20. Ben McCalman, 21. Nick Phipps, 22. Matt Toomua, 23. Kurtley Beale (56 Tests).