A pontoon barge supporting The City of Adelaide was towed from the Scottish Maritime Museum at Irvine on Friday.
The ship has been there since it was salvaged in 1992, after sinking the previous year in Glasgow's River Clyde.
The Adelaide was built in Sunderland in 1864. Its new Australian owners are having it towed to London, where a cargo ship will take it to Adelaide.
The planned start of the journey had been delayed from last week following adverse weather conditions in Ayrshire.
The pontoon supporting The Adelaide is now being towed out into the Irish Sea.
Over the next seven to 10 days, it will travel round the tip of Cornwall and up into the River Thames.
The historic clipper will then be loaded onto a cargo ship for its final journey to Australia.
The City of Adelaide was built on the River Wear to carry people emigrating to southern Australia.
In 1893 it became a hospital ship, but in 1924 was converted into a training ship at Irvine, and renamed HMS Carrick.
In 1991 the ship sank at the Princes Dock, Glasgow, and lay on the bottom of the River Clyde for a year before being raised and taken to Irvine.
For years, it lay rotting on a slipway at the Scottish Maritime Museum, with the cost of repairs put in excess of ??10m.
A rescue campaign mounted by rival consortiums from Adelaide and Sunderland saw the Australian group win the bid for ownership.
It formally took control of the Adelaide two weeks ago.
A crowd of up to 1,000 people has watched the world's oldest clipper ship leave Scotland for the last time.