The 62-year-old was dismissed by England in December after seven years in the role.
“It is a wonderful opportunity for me to be able to come home to Australia and lead my nation to a Rugby World Cup,” Jones said.
“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.”
Jones started discussions with Rugby Australia shortly after his sacking by the Rugby Football Union, and told the BBC last month he had “one last big job in him.”
However this had been expected to come about after the 2023 Rugby World Cup, so his appointment as Wallabies boss with immediate effect is a sensational development that will further shake up the international rugby landscape.
Rugby Australia’s swoop for Jones caps a remarkable period, with England, Australia and Wales all making major regime change a matter of months out from the Rugby World Cup.
All three nations are on the same side of the draw at the tournament in France later this year, with Jones’ Australia and Warren Gatland’s Wales in the same pool, and a quarter-final meeting with England a distinct possibility.
As part of his role, Jones will also oversee the Australia women’s team.
“It is a major coup for Australian rugby to have the best coach in the world return home to coach the iconic Wallabies and to oversee the Wallaroos program,” added Rugby Australia chairman Hamish McLennan.
“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 was appointed England boss in 2015 and won a Grand Slam in 2016 before reaching the World Cup final three years later, but he was dismissed in December following a poor run of form, with the side winning just five of 12 Test matches in 2022.
However his move to the Wallabies presents him with another opportunity to target the Webb Ellis trophy.
“The Wallabies squad is a really talented group of players with good depth,” Jones added.
“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.”
Rennie, 59, took over from Michael Cheika as Australia head coach in 2020 but has been dismissed after picking up just five wins from 14 Tests in 2022.