The Rock has made headlines since its unusual design was made public, with some saying it looked more like a group of pumpkins.
The largest of the three structures is 16m high and 33m wide and the building is encased in copper plating, which will change in colour as it is exposed to the elements.
The extension, the second stage of a five-year development, means the airport can cater for up to 1000 passengers per hour, as the departure lounge has doubled in size.
Infratil, which owns 66 percent of Wellington Airport, said the The Rock's design pushed new boundaries but was still functional and cost-effective.
The new gateway represented the capital's "unique and exciting spirit," Infratil director Lloyd Morrison said.
Wellington International Airport chief executive Steven Fitzgerald described the building as "unique, dynamic and functional".
Prime Minister John Key will open the new development today.
