The Sydney FC manager will take over from Dutchman Bert van Marwijk after the World Cup in Russia in June.
Arnold has been given a four-year contract until the end of the 2022 World Cup.
He had long been a favourite for the national role on the back of his record-breaking success with the title-winning Sky Blues.
The 54-year-old will leave the A-League club at the end of the A-League season in May, Sydney FC chairman Scott Barlow said.
“To be blunt, we didn’t want Graham to leave and we offered him a substantially bigger and longer contract to stay,” Barlow said in a statement today.
“But the lure of coaching his country has ultimately proven too much, and having complied with the terms of his contract, we would not stand in his way.”
Arnold said it was an “extremely difficult decision”.
“I love the club, the players and the fans so much and it was always my dream to coach Sydney FC,” he said.
“I am fully committed to the club, to the players and the fans until the end of the season and I am fully focused on achieving more success.”
Arnold’s initial major Socceroos’ task is an Asian Cup defence next January in the United Arab Emirates.
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