The building project provides a new entrance, with exhibitions, audio-visual facilities and interactive displays.
The contract to do the work was won by Rigg-Zschokke.
Building will largely be finished in June.
That will then be followed by the fit-out of the new reception area and shop.
Mr Gilberthorpe said further fundraising would then be done for "finishing touches" once visitors to the museum could see what had been achieved by the redevelopment.
About this time last year museum chairman Graeme Gray said Cobblestones had succeeded in trebling visitor numbers to reach around 3000 a year, but that the redevelopment of the front entrance was expected to greatly enhance that number.
He said closer links were being forged with Destination Wairarapa to help achieve that goal.
Included in the redevelopment were audio-visual and interpretive displays telling the stories of Wairarapa's early settlers.
Cobblestone Museum was originally the site of Cobb & Co stables with William Hastwell running a mail and passenger service from Wairarapa to Wellington in the latter part of the 19th century.
The complex takes its name from the cobblestone paving that still exists.
Greytown Jaycees were a driving force behind getting the museum started and nowadays the site includes many historic buildings, including Wairarapa's first public hospital, first Methodist Church, a colonial cottage and a shearing shed.