Premier Colin Barnett said the money from the sale of the former Sunset Hospital matron's house would fund Stage One of the redevelopment of the hospital's heritage-listed buildings.
"It's an interesting buyer, isn't it?" Mr Barnett said.
"It adds a bit of spice to the story.
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"He was one of the bidders and he bid the right price " there were no special conditions, no special deals."
Nedlands Mayor Max Hipkins said the council's preference was not to sell any of the buildings at the site.
He said the Government would need to spend at least $50 million to redevelop the old hospital buildings.
"It's disappointing in the total scheme of things," Mr Hipkins said.
"They expected to get more than $10 million for it.
"It would have been better, in my opinion, not to sell."
Mr Barnett said at 1993sq m, the site of the matron's house only made up 2 or 3 per cent of the total site.
"I've always had a special interest in this place because I grew up about 100m away," Mr Barnett said.
"The building dates from 1904 and was established as the Sunset Hospital but is generally known as Sunset Old Men's Home."
Mr Barnett said the buildings were heritage listed in 1997.
Finance Minister and Nedlands MLA Bill Marmion said Stage One of the redevelopment was expected to take 15 to 18 months.
He said future development would be in accordance with the City of Nedlands Town Planning Scheme.
"The Government has been trying to do something with it for 20 years," Mr Marmion said.
"Removal of asbestos will be one of the first things to happen."
Stage One will also include preservation and maintenance work on the buildings, upgrades to power, water, sewerage and gas services and landscaping the surrounding parkland with new picnic and barbecue facilities.
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