The 48-year-old, who represented the Socceroos four times as a player, has been given a five-year contract and will officially begin work on Monday, taking over from the sacked Holger Osieck.
"The Socceroos belong to the people of this nation," said Postecoglou. "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."
Postecoglou's first game in charge will be on November 19 against Costa Rica when he can begin his preparations for next year's World Cup in Brazil.
Postecoglou emerged as the number one choice from Football Federation Australia's three-man shortlist, which also contained Western Sydney Wanderers boss Tony Popovic and Central Coast Mariners' title-winning coach Graham Arnold.
Guus Hiddink was seen as favourite in some quarters to take over on a short-term basis after German Osieck was sacked, but FFA chairman Frank Lowy was pleased to turn to an Australian.
"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," said Lowy.
"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."
The Victory have made little secret of their displeasure at the manner in which FFA have handled the appointment.
But FFA chief executive David Gallop said: "The nation came calling for Ange and that left the Melbourne Victory chairman Anthony Di Pietro and his board of directors with a decision to make.
"Victory has done the right thing by Australian football and the club is to be commended."
Postecoglou has enjoyed domestic success, winning titles while in charge of South Melbourne and Brisbane Roar - the most recent of which came last year before he moved on to the Victory.
He will take over an Australia side which has faltered in embarrassing fashion after coming through a nervous World Cup qualifying campaign.
Back-to-back 6-0 defeats by Brazil and France cost Osieck his job, though they rebounded to beat Canada 3-0 in a friendly in London.
- Sports & Recreation
- Holger Osieck
- Australian football