Murphy's long-time Leicester team-mate, Martin Corry, captained the Baa Baas to a 33-26 win over England at Twickenham last Sunday and will start the Sydney game - his last before he retires - on the replacements bench.
Noted as one of the most naturally-talented backs in Irish rugby, the 31-year-old Murphy made his Barbarians debut eight years ago and is in his testimonial year with Leicester.
He played five times for Ireland this season, including a replacement appearance in the Grand Slam-clinching game against Wales in Cardiff.
The Barbarians side to face the Wallabies includes three players aligned to Irish provinces, although one of them, back rower Rocky Elsom, has just this week agreed to leave Leinster and return home to his native Australia.
Elsom's Heineken Cup-winning Leinster team-mate Chris Whitaker will partner All Black Luke McAlister at half-back, while Ulster's Springbok prop BJ Botha will pack down in a front row containing New Zealand's Clarke Dermody and Frenchman Sebastien Bruno.
Barbarians coach Dai Young said: "We want to throw the ball about (and) we want to be entertaining but make no bones about it as well, we want to win.
"It's a fine balance but one we can strike.
"But not only was the commitment there (against England) but I thought we scored some really good tries as well. Hopefully we can build on that this week."
Saturday's game, after which the winners will lift the Nick Shehadie Cup, will be broadcast live on Sky Sports 2 (kick-off 10.30am Irish time).
Australia have proven to be tough opponents for the Baa Baas. Indeed, the Wallabies have won the sides' last six meetings including an 18-11 victory at Wembley last December.
The Barbarians' last success in this fixture was back in 1976 in Cardiff (19-7).
BARBARIANS (v Australia): Geordan Murphy (Leicester Tigers & Ireland); Iain Balshaw (Gloucester & England), Sonny Bill Williams (Toulon), Seilala Mapusua (London Irish & Samoa), Josh Lewsey (London Wasps & England); Luke McAlister (Sale Sharks & New Zealand), Chris Whitaker (Leinster & Australia); Clarke Dermody (London Irish & New Zealand), Sebastien Bruno (Sale Sharks & France), BJ Botha (Ulster & South Africa), Chris Jack (Saracens & New Zealand), Paul Tito (Cardiff Blues), Jerry Collins (Toulon & New Zealand), Phil Waugh (Waratahs & Australia) (capt), Rocky Elsom (Leinster & Australia).
Replacements: Schalk Brits (Stormers & South Africa), Greg Somerville (Gloucester & New Zealand), Martin Corry (Leicester Tigers & England), Serge Betsen (London Wasps & France), Justin Marshall (Saracens & New Zealand), Glen Jackson (Saracens), Ben Blair (Cardiff Blues & New Zealand).