All 20 crew members aboard will undergo a "comprehensive health check," which will include testing when they arrive.
Most will then be transported to an MIQ facility to complete at least 14 days in managed isolation.
A small number of crew will complete their isolation period on board to meet the maritime safety requirements.
The Viking Bay had also been offered an anchorage at the Ports of Auckland.
Ports of Auckland earlier said it would not be taking the Spanish flagged fishing vessel Viking Bay "in-port" but would allow it access to its quarantine anchorage near Rangitoto Island.
However Customs' group manager maritime Stephen Waugh said that given the circumstances in this case, only a berth located within a port environment was suitable.
Waugh said the process announced today would carry very low public health risk.
"The crew will be transported at a time that will minimise the risk of coming into contact with members of the public," he said.
"Customs will maintain presence at the port throughout the operation, with the support of additional security personnel, and the Police Maritime Unit maintaining watch over the water."
Customs said that all Government and CentrePort staff that interact with the vessel or crew are vaccinated.
