The roof has recently been added to the twin-level, 3000sq m building, which constitutes the first stage of the planned four-stage museum redevelopment.
Construction work was on time and on budget, organisers said.
Bronwyn Simes, the museum project development manager, and senior representatives of project manager Octa Associates showed Dunedin Mayor Peter Chin and Dunedin city councillors around the $11.5 million complex recently.
The building will greatly improve protection of heritage treasures at the Dunedin City Council-owned museum, providing climate control for all its stored artefacts for the first time.
Paul Hudson, who chairs the council's community development committee, said it was satisfying to see greatly improved storage conditions becoming a reality.
Internal fit-out, including installing electrical wiring, is continuing.
The economic downturn has added to potential difficulties in raising some funds for the overall $35 million redevelopment project, although most of the required funding has already been allocated by the council.
City council community life general manager Graeme Hall said that, in addition to council funds already earmarked, considerable further funds had been raised from the Government and community sources for the project, including a $6 million government grant.
About $5 million more needed to be raised.
Having the storage building completed in November would boost fundraising efforts, enabling potential contributors to better appreciate what was intended for the multistage redevelopment, Mr Hall said.
The redevelopment is due to be completed in 2012.
