The former South Africa coach is contracted until after the 2015 World Cup in Australia and New Zealand.
He succeeds Tim Nielsen, who resigned after the tour of Sri Lanka in September, leaving bowling coach Troy Cooley in temporary charge.
"I am confident the talent is there to ensure Australia is successful," said the 43-year-old Arthur.Continue reading the main story Born: 17 May, 1968 in JohannesburgMajor Teams: Griqualand West, Orange Free State, South Africa AFirst-class batting record: 6,657 runs at 33.45Teams Coached: Griquas, Eastern Cape, South Africa, Western AustraliaTest record as South Africa coach: W22 D7 L16
Arthur coached South Africa from 2005 to 2010, leading them to a first series victory in England for 43 years and a maiden series win in Australia.
He quit in January 2010 after a fall-out with the national board and had most recently been in charge of Western Australia.
His appointment is the latest step in an overhaul of Australian cricket following their 3-1 Ashes humbling on home soil by England at the turn of the year.
Chairman of selectors Andrew Hilditch and selector Greg Chappell were both ditched, while former Australia rugby international Pat Howard was appointed Cricket Australia's general manager for team performance.
Arthur, who beat off competition from Australians Steve Rixon, Tom Moody and Justin Langer, said he felt comfortable about becoming the first foreigner to coach the side.
"I don't think it will matter," Arthur said. "Ultimately, I guess you want a guy that is perceived to be the best for the job, irrespective of the nationality."
Arthur is charged with reviving the fortunes of a team which has fallen to fourth in the world Test rankings after dominating the sport through the 1990s and early 2000s.
Australia fans were given hope for a brighter future on Monday when Michael Clarke's team pulled off a thrilling two-wicket victory over South Africa to tie the series, with 18-year-old fast bowler Pat Cummins producing a man-of-the-match performance on his debut.
"Australian cricket is in a very exciting phase [but] getting to the top of the Test rankings is something that just doesn't happen, because you need sustainable success over a period of time," said Arthur.
"We need a real good, strong squad system. I think young players need to be given quality opportunities to develop their games under pressure and hopefully we can create that environment for them to all perform."
Arthur, who will join a selection panel chaired by former Australian Test batsman John Inverarity, said it was too early for him to speculate on the future of older players like ex-skipper Ricky Ponting, who is 36.
"I'll defer that to the first selection meeting," Arthur said. "It's hard coming in from the outside without knowing what is going on. That's something for John Inverarity to take up."
Arthur's first series in charge will be a two-Test series against New Zealand, starting in Brisbane on 1 December, before Australia host India for a four-Test series starting on 26 December.