A ground-breaking event was being held today and Jones said that would mark progress in a 10-year plan for parcel growth.
NZ Post also announced today it was investing $170m in its network to double its parcel-processing capacity from 95m parcels to 190m parcels.
Jones said the developer and contractor expected to employ 350 people through 60 sub-contractors.
The investment programme will include a new processing centre in Auckland and an upgrade to the southern operations centre in Christchurch.
The Wellington super depot was due to open in 2022, Jones said.
Last month, Kris Faafoi, Minister of Broadcasting, said without the Government support NZ Post would face having to make drastic cuts to its mail business to remain viable.
"Post's revenue has fallen substantially but the costs of delivering the service New Zealanders expect have remained the same. The $150m equity injection, along with the $130m funding for mail services, means we avoid significant cuts to its service and workforce and big price increases for its customers," Faafoi said at the time.
In September last year, NZ Post reported a loss of $121m in the 12 months ended June 30, compared to a profit of $13m a year earlier when the bottom line was buoyed from its share of Kiwibank profits.
The latest period included a $51m impairment charge on the mail service assets, $38m being set aside to cover underpaid holiday pay, and a $15m settlement with ACC and the New Zealand Superannuation Fund over their purchase of 47 per cent of Kiwibank parent, Kiwi Group Holdings.