Ange Postecoglou has turned down the opportunity to become the first man to coach the Socceroos at two World Cup finals.

The 52-year-old announced on Wednesday that he was standing down as national team coach, a week after ensuring that Australia would qualify for a fourth successive World Cup following a 3-1 victory over Honduras.

Football Federation Australia will now begin the search for a new coach.

"After a great deal of thought and soul searching I've decided that the journey for me ends as Socceroos coach," Postecoglou said at a media conference in Sydney on Wednesday.

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"As I've said many times, it's been the biggest privilege of my life and it's probably not the ending I'd envisaged when we started - but at the same time knowing that it's the right time for me and the right decision."

Postecoglou thanked former and current FFA presidents Frank and Steven Lowy and federation CEO David Gallop for their support.

"It's a tremendous responsibility to coach your own nation and as an Australian I know how important it was that I was successful in terms of what we needed to achieve over the last four years," he said.

Postecoglou replaced the sacked Holger Osieck as Australian coach in late 2013 and took the national team to the 2014 World Cup in Brazil.

Steven Lowy and Gallop had been eager to retain Postecoglou as coach until the 2018 World Cup in Russia, even after he had hinted at grievances in the role.