The new permanent building will house the York Society research and archive centre at the corner of Avon Terrace and Ford Street.
A member of the York Society, the late Shirley Lutze, inspired the society to set up the archives group in 1987.
Since then, it has grown substantially, with more material donated by the public.
The York Society had a series of temporary homes, including the old courthouse, the town hall and, from 1996, the Old Convent, in South Street.
Arrangements were then made to house the archives to continue on a temporary basis on a privately owned outbuilding until a suitable permanent home could be found.
The new building received generous funding for its construction, including $278,000 from Lotterywest and $200,000 from the Shire of York.
Sir William, who was born in Fremantle, performed a range of roles for the Queen from 1965 until 1990, including press secretary.