The art work was commissioned in 2016 for the roof of Christchurch Art Gallery Te Puna o Waiwhetū, following the 2011 earthquake. It moved to its new home on top of the City Gallery in 2019.
Weather permitting, the sculpture will be removed from the City Gallery roof on Saturday.
Quasi is now returning to Australia, to a venue which is yet to be disclosed. Ronnie van Hout, born in Christchurch, is now living in Melbourne.
The sculpture is one of the most recognisable in the capital, with the 5m tall hand standing on two fingers with the artist's face protruding from the back. It is a partial self portrait, based on scans of the artist's face and hand.
The art work references Quasimodo, the bellringer in Victor Hugo's 1831 novel The Hunchback of Notre-Dame.
"No other, before or since, arrived so dramatically into our street-scape. Quasi arrived on an azure-blue morning by helicopter and created a stir from day one, locally, nationally and internationally.
"He was a great cheerleader for Wellington's creativity, and as TIME magazine said, our 'quirkiness'.
"He will be missed and leaves a Quasi-shaped hole on our civic skyline."
"Quasi will continue to bring his big personality wherever he goes. It's been a privilege to share our home with him for five years."
The City Gallery has closed for two years due to construction work in Te Ngākau Civic Square, as well as building repairs, and is due to reopen in 2026. Cooke said it was still offering exhibitions at other locations.