Hooker Ford and lock Gray were suspended for three weeks for a dangerous tackle on Samoa's Jack Lam in their final Pool B match. Scotland have appealed against the length of their bans.
Blair Cowan comes in at openside flanker for Ryan Wilson while the one change in the backs brings in Peter Horne at inside centre for Matt Scott, who dropped out with back pain.
Kevin Bryce and Alasdair Strokosch are on the bench to take the spaces in the 23 vacated by Brown and Swinson.
"It’s always nice to be part of the final eight of any qualifying competition, the guys are very excited about being here," coach Vern Cotter said in a Scottish Rugby statement.
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“We will go into this game with the belief that we can compete with and dominate a very strong Australian team and move forward to the last four.
“They are a front-foot momentum team so defence will be key, but also getting our hands on the ball and expressing ourselves as we like to."
Brown said that Scotland had the character to overcome the loss of Ford and Gray as they look forward to the knockout stage after missing out four years ago.
“It is tough for Fordy and Jonny, but we’ve spoken about it with them. When they initially got cited we prepared for it and from Tuesday we focused on the weekend," he told a news conference.
“Ross has been around the block long enough and he has dealt with it by throwing himself into helping us prepare as well as possible and allowing us to get ready.
“It is what I’ve been preparing for for the past two years and it is going to be a huge opportunity for us to go out there and do something we haven’t done for some time."
The Wallabies won the last clash between the teams in 2013 at Murrayfield, but Scotland emerged victorious in Australia in 2012 with a thrilling 9-6 success, having also claimed a 9-8 win in Edinburgh in 2009.
Team: 1-Alasdair Dickinson, 2-Fraser Brown, 3-WP Nel, 4-Tim Swinson, 5-Richie Gray, 6-Blair Cowan, 7-John Hardie, 8-Dave Denton; 9-Greig Laidlaw (captain), 10-Finn Russell, 11-Tommy Seymour, 12-Pete Horne, 13-Mark Bennett, 14-Sean Maitland, 15-Stuart Hogg
Replacements: 16-Kevin Bryce, 17-Gordon Reid, 18-Jon Welsh, 19-Alasdair Strokosch, 20-Josh Strauss, 21-Henry Pyrgos, 22-Richie Vernon, 23-Sean Lamont
(Reporting by Justin Palmer; Editing by David Goodman)
