The City of Adelaide, built in 1864 to take migrants from Europe to Australia, is voyaging south for the first time in around 125 years.
The boat has been kept on a slipway at Scottish Maritime Museum in Irvine, North Ayrshire since 1992 after sinking in the River Clyde the previous year.
The museum could not afford to refurbish the ship and applied to demolish it.
The new owner, charitable organisation Clipper Ship City of Adelaide, led a successful campaign to save and relocate the boat which will go to a maritime heritage park in South Australia. The group beat a rival bid from campaigners in Sunderland where it was built.
The clipper's papers were handed over at a ceremony at the museum's Linthouse building before it begins the first leg of its 13,670-mile (22,000km) journey.
Sam Galbraith, chairman of the museum's trustees, said: "The voluntary group Clipper Ship City of Adelaide Ltd have worked carefully and methodically to reach this stage and demonstrated that they had the technical skill and knowledge to complete the conservation of the vessel.
"Although the vessel was departing to Australia, arrangements are in place for the further development of long-term links between the project, South Australia and Scotland and the UK."
Clipper Ship City of Adelaide director Peter Christopher said: "The movement of the City of Adelaide reflects not only a remarkable engineering feat but also demonstrates what can be achieved through co-operation.
"Faced with the prospect of the vessel being deconstructed, the Scottish Government, to its credit, decided to explore other options. The relocation of the ship to the city after which it was named is an appropriate solution to a difficult problem, and one which will benefit future generations in both our countries."
Jim Tildesley, the museum's ex-director and coordinator of the project, organised the rescue of the boat when it sank in the Clyde. He said he has no regrets seeing it depart.
"Having worked in museums all my working life, our job is to pass the heritage on to the future, and we are passing it on to an organisation that is going to have more resources to look after it," he said.
The 450-tonne clipper will carry as its last cargo the letters of school children from across the UK to their counterparts in Australia, as part of a cultural exchange.
The A-listed structure was once regarded as unrecoverable due to the silted river and protected wetland areas around its berth in Irvine, but engineers in Australia created a steel cradle to allow the ship to be rolled across a temporary bridge over the river surface and on to a low-draft barge.
The City of Adelaide is due leave Scotland in days. The barge will take it to Greenwich in south-east London where it will moor beside sister ship the Cutty Sark. It will then be lifted into the hold of a cargo ship to go to Australia. It is due in Adelaide next spring.