The urn has been displayed in Australia on only one previous occasion, in 1988 to help celebrate the bicentenary of European settlement, but will now be shown around the country to coincide with the 2006-07 Test series between Australia and England.
The exhibition will visit six museums in five cities, starting in Sydney and ending in Melbourne, over a 14-week period commencing in November.
An exhibition that had been planned for 2002-03 had to be cancelled when X-rays revealed serious cracks in the urn's shoulders and stem.
But restoration work has since taken place and MCC now believe the urn, although still fragile, can be flown from England to Australia.
"In 2005 alone, more than 35,000 people - from all over the world - came to the MCC Museum at Lord's, where they could see the Ashes urn for themselves," said MCC curator Adam Chadwick.
"This touring exhibition will enable many more Australian cricket lovers, right across the country, to see the urn and learn more about its long and fascinating history.
"We are particularly pleased to be staging this tour, after our previous plans had to be cancelled.
"MCC looks forward to working closely with the six museums chosen to stage a great exhibition which will, we hope, be seen and enjoyed by tens of thousands of people."
Last year England regained the Ashes with a thrilling 2-1 home series win and their upcoming tour of Australia will be the first time in 20 years that they have arrived 'Down Under' to defend them.
The term "Ashes" was coined after England lost a Test to Australia for the first time on home soil at The Oval on August 29 1882.
A day later, The Sporting Times carried a mock obituary to English cricket which concluded: "The body will be cremated and the ashes taken to Australia."
The Ashes urn was subsequently presented to Ivo Bligh (later Lord Darnley), who captained the next English team to tour Australia.
He subsequently took the urn back to England, where it was kept at his family home in the south-east county of Kent. On his death, in 1927, his widow bequeathed the urn to MCC.
As well as the urn itself, the exhibition will feature other Ashes-related artefacts. They will include the velvet bag presented to Bligh in which he kept the urn and the original scorebook from the 1882 match at The Oval.
It has long rankled with Australian fans that the Ashes always stay at Lord's regardless of which team has won the series.
MCC tried to tackle this issue by commissioning a crystal Ashes Trophy, also set to be part of the exhibition. This was first presented at the end of the 1998-99 series to then-Australia captain Mark Taylor but is now currently in England's possession.
One reason why the Ashes have not been taken to Australia more often is that MCC have argued they were a private gift not a sporting trophy.
Ashes Exhibition Itinerary
Oct 21-Nov 08: Museum of Sydney, Sydney
Nov 12-Nov 22: Queensland Museum, Brisbane
Nov 26-Dec 06: South Australia Museum, Adelaide
Dec 10-Dec 20: Western Australia Museum, Perth
Dec 26-Jan 07: Melbourne Museum, Melbourne
Jan 09-Jan 14: Melbourne Cricket Club Museum, Melbourne Cricket Ground