Van Marwijk took the Netherlands to the final last time he coached at a World Cup in 2010.
His last job was in charge of Saudi Arabia, where the Dutchman pipped Ange Postecoglou's Socceroos to second place in their Asian qualifying group, sending Australia into playoffs with Syria and Honduras.
The 65-year-old claimed the role ahead of big-name Roberto Mancini, Marcelo Bielsa, Jurgen Klinsmann, Slaven Bilic and Louis van Gaal.
His biggest coaching achievement was reaching the 2010 final with the Netherlands, lost 1-0 to Spain in extra time.
Van Marwijk has less than five months in charge ahead of Australia's opening match with France but he said his ambition at June's World Cup went beyond making up the numbers.
"We are not going to Russia just to be competitive. I want to win our matches," he said in a statement.
"I know a lot about the players and how the team has been playing after coaching against them for the two World Cup qualifiers, in 2016 and in June last year.
"I have also been impressed by the national team setup that the FFA has developed over the past few years."
FFA chairman Steven Lowy trumpeted his appointment.
"This is a great result for Australian football," he said.
"Bert Van Marwijk is world class. He took the Netherlands to the World Cup final in 2010, he led the Saudi Arabian team to qualify directly for this year's finals and most importantly, he knows a lot about our team and how they play because he studied them closely as an opposition manager in the same group.
"These experiences make him a compelling choice."
His appointment continues a trend of Dutchmen taking charge of the Socceroos.
Guus Hiddink led Australia to the 2006 tournament, reaching the second round and earning the moniker of 'Aussie Guus' for his impressive tenure.
Pim Verbeek enjoyed less success in charge of the side from 2007-2010, failing to get out of the group at the South Africa tournament.
FFA Chief Executive Officer David Gallop agreed terms with the former Netherlands national team coach in Amsterdam.
Speaking from Amsterdam, Gallop said: “Bert was our preferred candidate to take the Socceroos to the World Cup so we are delighted to have secured his services.
“We went through a thorough and disciplined process and used internal and external experts to build up a profile of the person who would be the best fit for the task in Russia. We had a number of outstanding coaches very interested in the role but Bert was at the top of our shortlist.”
The FFA confirmed arrangements for who will take over the Socceroos after the World Cup will be announced in the near future.
Sydney FC coach Graham Arnold is the strong favourite to take over long-term.