The restored 19th century tea clipper, permanently moored in south-east London, will be open to the public from April 26.
It follows the raising of its masts in December – the first time since the fire in May 2007.
The £10million fire was caused by an industrial vacuum cleaner which was left switched on.
At the time, the 143-year-old ship was undergoing a conservation project to halt the erosion of its iron framework.
Because of this, much of the ship had already been removed and put into storage.
“Thanks to heroic firefighting, there was amazingly little damage to the ship’s original fabric,” a spokesman for the Cutty Sark Trust said.
The restoration has come to a total of £50m.
The Cutty Sark left London on its maiden voyage on February 16, 1879, sailing around The Cape of Good Hope to Shanghai in three-and-a-half months.
The vessel made eight journeys to China as part of the tea trade until steam ships replaces sail on the high seas.
It then served as a training ship for naval cadets during World War II.
In 1951 it was moored in London for the Festival of Britain.
It has been berthed in Falmouth and Greenhithe, but has not been moved from Greenwich since 1954.