It was one of the largest design-and-build projects the Hawke's Bay-based construction company had handled in recent years, he said.
"Combining the design and build functions is an approach that is gaining momentum in the construction industry and we are pleased to be at the forefront of that movement. It gives us the flexibility to work with design consultants who share the same vision as we do for our client."
The build will provide at least 40 jobs.
Napier Port prides itself on its safety record and the new administration building will have a dedicated entrance. The current offices require visitors to share lanes with heavy machinery, some carrying shipping containers.
Local structural engineers Structural Concepts have joined Alexander Construction on the project.
Mr Hamilton expects port staff to be in their new building in early 2015. The existing gate house will be transformed into a gymnasium, connected to the new structure by a footbridge.
The administration building is located on a site formerly used for container stacking.
Alexander Construction's growing portfolio of projects includes a fire station redevelopment in the Chatham Islands.
The port has recently struggled to cope with a spike in apple shipments in containers, with some exporters diverting fruit to other ports.
Napier Port chief operating officer Chris Bain said the port needed to "significantly invest to boost container terminal capability within the next nine to 10 months.
"Replicating how we currently operate is unlikely to bring the level of service and capacity future-proofing now needed."
Napier Port has capital expenditure of $150 million planned for the next 10 years to cope with expected growth due in part to it winning business from other ports.
Its growth has been consistent for several years despite the regional economy's slump, due to winning other ports' business.
The port is owned by the Hawke's Bay Regional Council.