Adams, the only new name in the backline, starts on the left wing, taking the number 11 jersey off Luke Morgan after the 21-10 win over Scotland.
Beard comes in at lock, where he will partner skipper Alun Wyn Jones, with Cory Hill dropping to the bench.
Despite Dillon Lewis’ strong performance against Scotland, he too is amongst the subs. He has been replaced by Francis in the absence of Samson Lee, who is out with a hamstring injury.
Having missed last weekend’s game, Dan Biggar comes onto the bench, where he is accompanied by another star name in Liam Williams. In total, the Welsh bench boasts 185 caps.
“We were pleased to get a good opening win under our belts last weekend and this Saturday is all about building on that,” said Wales head coach Warren Gatland.
“With selection we wanted some continuity and to be consistent but also mindful there are a number of players who did really well for us in the summer and they need to be rewarded and have their opportunity.
“Adam (Beard) impressed in the summer as did Josh (Adams) and they deserve the chance to start.
“There is a really good balance to the team, a lot of competition which is exactly what we wanted.
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“The bench is packed with quality and experience and it will be great to see them have an impact on Saturday.”
Wales are unbeaten in six matches, but they will be up against a Wallabies side that has beaten them in 13 consecutive Tests.
Nevertheless, with Australia having lost seven out of 10 Tests in 2018, Wales arguably head into the match at Cardiff’s Principality Stadium as favourites.
Wales: 15 Leigh Halfpenny, 14 George North, 13 Jonathan Davies, 12 Hadleigh Parkes, 11 Josh Adams, 10 Gareth Anscombe, 9 Gareth Davies, 8 Ross Moriarty, 7 Justin Tipuric, 6 Dan Lydiate, 5 Alun Wyn Jones (c), 4 Adam Beard, 3 Tomas Francis, 2 Ken Owens, 1 Nicky Smith
Replacements: 16 Elliot Dee, 17 Rob Evans, 18 Dillon Lewis, 19 Cory Hill, 20 Ellis Jenkins, 21 Tomos Williams, 22 Dan Biggar, 23 Liam Williams
Date: Saturday, November 10
Venue: Principality Stadium, Cardiff
Kick-off: 17:20 GMT
Referee: Ben O’Keeffe (New Zealand)
Assistant referees: Romain Poite (France), Brendon Pickerill (New Zealand)
TMO: Simon McDowell (Ireland)