The development will include 10,000-square-metres of workspace and rooftop gardens.
It will have a sinuous, looping form that slots into the boundaries of its roadside site, and nods to the seven bridges and hilly landscape for which the city is known.
"Our proposal is born from the unique conditions of Newcastle's architectural elements, the sloping hills and the curvy frames of the bridges over the Tyne," said BIG founder Bjarke Ingels.
"The ascending serpentine silhouette feels like a fresh yet familiar continuation of this unique urban landscape," he continued.
"It follows the hairpin curve of the road and becomes a ribbon-like building climbing up the hill side while creating a cascade of roof terraces overlooking the Tyne," added Andreas Klok Pedersen, partner at BIG.
No 1 Quayside is BIG's first UK project out of London, and has been designed for estate agent Knight Frank.
It will replace a nightclub that currently occupies the sloping site close to the River Tyne, which is flanked by roads on either side.
Though details of the office's interior design is yet to be disclosed, the floor area of each storey will decrease in size as the building winds upwards – reducing from 1,260 to 109 square-metres.
This will provide each of the 12 storeys access to a private garden on the building's stepped rooftop, and offer unobstructed views of the River Tyne throughout.
The roof gardens will all be lined with greenery, and connected via a staircase running along its edge.
Once complete, No 1 Quayside is hoped to become a landmark for the city that is currently best known for The Sage Gateshead by Foster + Partners and the bridges spanning the river, including the Gateshead Millennium Bridge by WilkinsonEyre.
BIG is an architecture practice founded by Danish architect Ingels in 2005, and has studios in Copenhagen, New York, London and Barcelona.
It opened its UK office four years ago to develop Google's EU headquarters with Thomas Heatherwick.
Elsewhere, BIG is working on a gateway building for Milan's CityLife district and collaborating with Toyota on the "city of the future" beside Mount Fuji in Japan.