Works at Lews Castle include fitting out the visitor and hospitality areas on the ground floor of the castle, along with the creation of luxury accommodation on the upper floors.
The project will progress in 2015, with the public opening of the new facilities being phases around these works.
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In addition, the new archive will be open to the public early in the New Year.
Following the installation of the British Museum and National Museums Scotland, loan objects the museum will fully open to the public.
Angus Campbell, Comhairle Leader and Chair of the Project Board said: "This is a hugely exciting and important project for the Comhairle and the community.
"The Comhairle's Heritage Team is working with a range of specialists and national partners to complete the development. There are stringent conditions attached to the long-term loan of priceless objects and we are enhancing certain aspects of our security system to achieve best practice.
"These additional measures will be delivered over the next few weeks and thereafter we will be in a position to confirm the opening date of the museum."
(LM/CD)
