The move has been in motion since late 2017 and is part of the developments around the University of Tasmania's Inveresk campus.

NAMT manager Phil Costello said the building is getting close to being able to store vehicles.

"Obviously we can't put cars in it until it's alarmed and everything," he said.

"It's virtually at lock-up, it's more or less finished we've got heaps of work to do inside it but the building itself is pretty much finished."

The museum has been located at its Cimitiere Street venue for more than 20 years.

It is home to more than 100 vehicles and receives about 24,000 visitors per year.

The new museum will include a warehouse, shop, display room, amenities and an office.

The nearly 2000 square metre building will be accompanied by two car parks which include 52 individual spaces as well as disability access.

Mr Costello said he expects the museum to be open in September.

"As far as opening it goes, the plan is to have it [the museum] open at the end of September," Mr Costello said.