The 12-level building has been in Government hands since it was built in the 1960s. Argosy will also now undertake extensive upgrading of the 24,977sq m structure.
NZ Post and Argosy said the sale would settle next Thursday "with a subsequent development period to provide a significant upgrade of the building to be completed by January 2016".
"The development will be completed in stages with New Zealand Post remaining in occupancy during the development period," the two said in a joint NZX statement.
Argosy chief executive Peter Mence said the property was bought partly for its location, between Parliament, Wellington Railway Station, the waterfront and the Lambton Quay shopping strip.
NZ Post has an evergreen lease on the building, meaning it could occupy it for a 40-year term but once refurbishment is complete, it can give Argosy notice to vacate within five years. The building was not earthquake-prone but some aspects of the planned work would see it strengthened, Mence said.
Contracts will soon be awarded for the $40 million upgrade which could involve installing new thermo-glass cladding on the exterior, see the tower tied to the podium level when columns are strengthened with steel and involve new services such as lifts and lighting being installed.
Argosy's $890 million portfolio would be worth $1.08 billion once that deal and another is concluded and two Wellington buildings are refurbished, Mence said.
In December, Argosy announced it would raise up to $100 million to buy the NZ Post property and 15 Stout St, formerly the Ministry of Defence building also in Wellington. Both deals were backed by long-term Government tenancies, Argosy said.
Argosy paid $33.2 million for the Stout St property and is spending $86.6 million upgrading the two buildings.
The company's shares closed unchanged yesterday at 99c.
Chris Dibble, Colliers International's Auckland research manager, said the NZ Post sale was a vote of confidence in the Wellington office investment market.
"The positives outweigh any short-term negatives - the slight dilution of shareholding in the first instance given the equity raising and share purchase plan, together with the significant seismic strengthening that is required, estimated at $40 million," Dibble said.
"However, over the long-term the benefit of having such a prominent office investment with a strong covenant that provides a 20-year lease and three-yearly market reviews will be earnings accretive," he said. Strengthening work expected to be completed in early 2016 will not detrimentally affect tenant operations who will reportedly continue to occupy the building throughout.
The latest Colliers International Confidence Survey for the March quarter showed that out of Wellington, Auckland and Christchurch, Wellington office investors were still the most pessimistic, with confidence at a net minus 5 per cent.
2013 biggest deals
• NZ Post House, Wellington, sold for $60m to Argosy.
•15 Stout Street, Wellington, sold for $33.2m to Argosy.
•Two New Zealand Post properties, sold to Manson TCLM, for a combined value of around $33m, at 151 Victoria Street, Auckland.
•Orion House, Grafton Rd, Auckland, sold to Oyster, $21.5m Source: Colliers International