The company's Dunedin franchise owner, Adam Cullen, said construction of the first of the new units (pictured) began in September.
The building is already leased by window and door makers Aitken Joinery.
Construction is expected to be finished and the new tenants inside before Christmas.
The other two buildings are expected to be completed by about April next year.
Mr Cullen said Speedy Signs needed more space after taking over the Queenstown Speedy Signs franchise, which closed due to Covid-19 disruptions.
That, and a busy period after lockdown making signs and screens related to Covid-19, were the key reasons behind the company’s expansion in Dunedin.
Staff had been ‘‘really busy doing general signage for Dunedin and New Zealand businesses, who for the most part seem to be doing very well’’, Mr Cullen said.
Much of the larger work for Queenstown and around the country will be carried out at the company’s Dunedin factory.