The five-year agreement runs until August 2018 with Postecoglou's term to include the 2014 FIFA World Cup in Brazil, the 2015 AFC Asian Cup on home soil and the 2018 FIFA World Cup Asian qualification matches.
"It was always our plan that one day an Australian would be appointed coach, and I said precisely that when we appointed the previous coach," FFA chairman Frank Lowy said.
"But I have never taken the view that the coach should be an Australian for the sake of having an Australian. I have always believed we should get the best person we can for the job.
"The fact that Ange is the best qualified, and an Australian, achieves our objective."
A delighted Postecoglou, 48, said he was honoured to be given the job of leading his country.
"The Socceroos belong to the people of this nation," he said. "It’s my job to make sure we represent all that’s good in Australian football. "We need to strive for greatness, to play with spirit and have an unwavering belief in our mission.
"I was proud to represent my country as a player and I have the same immense feeling of pride today.
"I thank Frank Lowy, David Gallop and the FFA for having the faith in my ability to do this job successfully."
An agreement to release Postecoglou from his contract with Melbourne Victory, after robust discussions with FFA, was sealed on Tuesday and he will officially begin his term as Socceroos boss on Monday - after signing off in the A-League with Friday night's encounter against his former side Brisbane Roar at Etihad Stadium.
"Ange Postecoglou has had a profound impact on Melbourne Victory Football Club over the past 18 months and the club is extremely appreciative of everything he has implemented during his tenure," Victory chairman Anthony Di Pietro said.
"Ange’s appointment as Socceroos coach is a fantastic endorsement for our club, its culture and the standards we strive to set. We thank Ange and he will certainly always be part of the Melbourne Victory family."
Postecoglou's first game in charge of the Socceroos will be against fellow World Cup qualifier Costa Rica at Sydney's Allianz Stadium on Tuesday 19 November.
The World Game live-tweeted the official announcement this afternoon.
"We might be able to unearth a number of young players who can have a big impact in years to come." - @Socceroos coach Postecoglou #sbstwg
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