Dismissed as England boss in December, with Steve Borthwick brought in as his replacement ahead of the Rugby World Cup this year, Jones has taken the Wallabies job for a second time.
Australia ditched Dave Rennie to create the vacancy, with Jones describing his return to the job he previously held from 2001 to 2005 as "a wonderful opportunity".
Rugby Australia said Jones has committed until 2027, meaning his contract covers two World Cups and the 2025 British and Irish Lions tour.
The 62-year-old, who was in charge of the Australia side that lost to England in the 2003 World Cup final, will formally start his second tenure on January 29.
Jones said: "It is a wonderful opportunity for me to be able to come home to Australia and lead my nation to a Rugby World Cup.
"It is going to be an immense period for Australian Rugby – as a proud Australian, it is a great honour to be able to come home and lead the national team during these years.
"The Wallabies squad is a really talented group of players with good depth – if we can have everyone fit and healthy going into the World Cup this year, I am confident that we can go to France and break the 24-year drought of winning the Rugby World Cup.
"I am really looking forward to getting back home and getting stuck in."
Defeats in November to France, Ireland and particularly Italy sealed Rennie's fate. His team also beat Wales and Scotland on their Northern Hemisphere tour, but those victories were not enough to save his job.
New Zealander Rennie had three years as head coach, and Rugby Australia said there had been "positive steps" taken under his leadership.
It was decided, however, that with Jones available for hire, Australia could not afford to stand by and see someone else move for him.
Rugby Australia chairman Hamish McLennan described the appointment as "a major coup", labelling Jones, who has also coached Japan, as "the best coach in the world".
"Eddie's deep understanding of our rugby system and knowledge of our player group and pathways will lift the team to the next level," McLennan said.
"Eddie instinctively understands the Australian way of playing rugby – this represents an opportunity to secure a coach of immense expertise and experience at the biggest competitions, and we did not want to miss it."
Jones will also oversee the development of Australia's women's programme, with the Wallaroos looking to build on a quarter-final appearance at last year's World Cup.