The building, which includes three vehicle parking areas as well as expanded storage facilities, replaces earlier garages, which were more than 40 years old and were demolished about six weeks ago.
University property services manager Barry MacKay said the new complex occupied the same 70sq m footprint as the previous garages, and was of timber-framed construction on concrete slab.
The new pitched truss roof allowed for extra storage space in the attic area.
Construction was expected to be completed within the next few weeks, Mr MacKay said.
Exterior maintenance work, including roof repairs and repainting, is also continuing at the New Zealand Marine Studies Centre, which is part of the complex. Internal repainting at the laboratory is planned for later in the year.