Postecoglou is set to leave Scottish champions Celtic for Spurs in the coming days, with the north London club offering the Australian a two-year deal with incentives for a third season.
Postecoglou would be the first Australian to manage in the Premier League.
Arnold, who has coached alongside Postecoglou at national team level and against him in the A-League, says one of the 57-year-old's greatest assets was his sharp eye in the transfer market.
Tottenham, under prudent chairman Daniel Levy, have developed a reputation for being frugal but Arnold declared Postecoglou has the ability to turn rocks into diamonds.
"I think one of Ange's huge strengths is recruitment and attention to detail," Arnold said, after naming his Socceroos squad for their June 15 friendly against Argentina.
"He finds players for the system he wants to play.
"I think it's a great job for him and I think he'll kill it."
When he first made the move to Glasgow, Celtic fans were initially sceptical of Postecoglou's resume.
But two seasons and five trophies later - in which he was lauded for his smart work in the transfer market - the Australian has won Celtic's fervent supporters over.
"He's totally obsessed with the game, it's his life and I always knew he had that mentality of getting to the top," Arnold said.
"He has had setbacks but you learn from those setbacks and Ange has always been determined to prove the doubters wrong and that, in a lot of ways, is his motivation.
"Me and Ange are mates and we were competitors against each other but to see what he's doing is brilliant."
Arnold said the rise of Postecoglou, as well as Joe Montemurro, Kevin Muscat and Patrick Kisnorbo to leagues with stronger reputations was an endorsement of the quality of Australian coaching.
"We might not be that bad, hey," Arnold said.
"These guys will end up overseas and Ange is the leader of that pathway.
"You need someone to open the eyes of people around the world to say; 'Australian coaches might not be so bad'. Ange has done that fantastically for all of us."
