Outgoing governor-general Sir Peter Cosgrove buys in Milsons Point

Sir Peter Cosgrove, who will step down as Australia's governor-general next month, and wife Lady Lynne Cosgrove, are downsizing in Sydney's north.

They will vacate the governor-general's official residence, Admiralty House on the Kirribilli waterfront, and will be moving in to a three bedroom apartment in Milsons Point.

Records show they paid $2.25 million for the 15th floor apartment in the Pinnacle building.

The apartment had sat idly on the market for around 50 days through Di Jones agent Nigel Mukhi, prompting the vendor to attempt the lease the investment apartment again at $1,500 a week before the Cosgrove's swooped.

The Pinnacle building was built in the late 1990s on Dind Street.

The Cosgrove's have called the lower north shore home for over a decade, having bought a Neutral Bay townhouse for $1.95 million in 2007.

They sold it for $2.1 million in 2014 given Peter's appointment as governor-general and the luxury of moving in to the 1840s Victorian sandstone Admiralty House.

The property on the tip of Kirribilli was built in 1842 by Lieutenant-Colonel John Gibbes. It was bought by the colonial government in 1885 and renamed Admiralty House.