Her assistant referees will be Mikael Berchebru and Aurelien Drouet, whilst the fourth official will be Hakim Ben El Hadj.
VAR Mathieu Vernice and assistant VAR Nicolas Rainville complete the line-up of French officials.
Frappart, who has been on the FIFA international referees list since 2009, has refereed several high profile matches.
The 39-year-old made history during the men's 2022 World Cup in Qatar, becoming the first woman to referee a men's World Cup fixture, taking charge of Germany's 4-2 victory over Costa Rica.
Now, she'll make another milestone when leads out the officials at Wembley this week.
In a statement on her appointment, the FA's head of refereeing operations, Peter Elsworth, said: "Stephanie is an outstanding referee and she has officiated on the highest stage within France, across Europe and recently at the men's and women's FIFA World Cup.
"We're delighted she and her team will take charge of our upcoming fixture against Australia in front of a sold-out crowd at Wembley Stadium and we're looking forward to welcoming them to the home of English football."
Aside from being the first female referee at a men's World Cup, Frappart has been a trailblazer across other competitions too.
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She often takes charge of Ligue 1 and Ligue 2 fixtures and was also the first woman to officiate in the men's Champions League and UEFA Super Cup.
England will be looking to use the fixture against the Socceroos to gear up for their Euro 2024 qualifier against Italy just four days later.