City councillors have agreed to strengthen the building with base isolators, which is expected to cost $187.4 million.
Paul Perniskie, Te Matapihi project director, said he's pleased with the "careful and professional operation" undertaken over the last five months by Ceres New Zealand.
Opened in 1991, the library is listed as a category 1 historical place – the first from the 90s. It's considered significant due to its architecture by Ian Athfield.
Chirag Sehgal of Ceres New Zealand said the operation was delicate and intensive, as the flood loadings were not significant to support such large machinery.
"We also kept to a rigorous waste minimisation plan – much of the material we removed has been reused."
The new design for the library is lighter and brighter as it has an additional light shaft to bring in the sunshine.
The design also proposes new entrances from the City to Sea ramp and another on the corner of Harris St. The main entrance on Victoria St will remain.
The design team included Athfield Architects, who designed the building originally; Aurecon, RCP, RLB, Tihei, Art of Fact, and Māpuna.
LT McGuiness has been selected to carry out the construction and plans to prepare to begin earthworks early next year, depending on the resource consent process.