Renamed HMS Carrick in 1922, she was berthed in Glasgow for 69 years as a floating naval club. Launched in 1864, she is the world's oldest clipper and the only surviving sailing ship to have carried migrants to Australia.
The vessel was prepared for her final journey at the Scottish Maritime Museum in Irvine, North Ayrshire.
David Mann, director of the museum, said: "We are very pleased she has reached her new home in Adelaide and that she will become an important part of culture there.
"It's nice that she travelled there as a working vessel and is now there for people with historic ties to her to see and cherish."
The clipper arrived in Adelaide aboard the vessel Palanpur at 8.50am local time on Monday, just around midnight UK time.
The voyage ended an extraordinary 14-year campaign by engineers, maritime historians, ship enthusiasts, descendants of the ship's migrants and supporters to secure the vessel for Australia.