The Socceroos, who lead their qualifying group, will face the leading African ranked team in Sydney on 23 May, FFA said.
Ghana, listed 15th on the FIFA/Coca-Cola World Ranking, begin their qualifying for the 2010 FIFA World Cup in South Africa at home against Libya on 30 May.
Australia will play their remaining Asian Group One games in June, starting with a home match against Asian Cup champions Iraq in Brisbane on 1 June.
The Australians will then face Iraq in the return fixture in Dubai on 7 June and Qatar in Doha on 14 June before returning home for a match against China in Sydney on 22 June.
Australia are unbeaten in their opening two qualifying World Cup matches, defeating Qatar 3-0 in Melbourne and drawing 0-0 with China in Kunming last week.
The top two teams in each group will progress to the fourth and final phase of Asian qualifying for the 2010 FIFA World Cup.
Sydney will also host the FIFA Congress on 29 and 30 May.