The parts were brought in through the main terminal doors before being clamped together and painted on-site.
It took three nights to construct the sculpture and attach it to the terminal's trusses with 10 suspension wires.
Sir Richard said Weta was thrilled to create something with the airport that would bring delight to the many visitors to the city.
"This sculpture is the best sort of thing we can be asked to build because it uses all of the artistry and crafts of the people in the workshop.
"This is a combination of incredible hand skills, with the carving of the polystyrene, but also the robotic engineering that is used in the workshop - machines built and developed by technicians on the workshop floor that allow sculptures of this scale to happen in the time required.''
Sir Richard said Weta had a long and wonderful relationship with the airport, having created memorable sculptures for the terminal in the past.
Airport chief executive Steve Sanderson said Twitter was alive with comments and photos which proved the sculpture was already a success.
Weta's Rob Gillies directed the creation of the sculpture using 3D modelling.
It was created using digital and physical techniques by a team of 18 sculptors, model makers, painters and other specialists.
The huge blocks of polystyrene were supported by a structure of scaffolding pipe which was designed to bolt together.
The sculpture features three 4m fish, which were hand-sculpted using a fish sculpture from Sir Richard's bathroom as reference.
It also features nine bubbles coming from Gollum's mouth and window decals designed to represent the stream.
The first part of the Sir Peter Jackson-directed trilogy, An Unexpected Journey, will have its world premiere in Wellington on November 28, before going on global release on December 14.
Wellington is spending $1.1 million on activities in the week of the premiere, billing itself as The Middle of Middle-earth.
