The town hall will be converted in the Â£3.1m project.
The scheme has received support from the Heritage Lottery Fund and Dumfries and Galloway Council.
Once completed it is hoped the building could become the home to the Viking treasure unearthed in the region more than two years ago.
Councillor Jane Maitland, whose ward includes the town, said it was an important day for the area which is proud of its history as an "artists' town".
"Of course I feel amazingly excited and enthusiastic about it all happening," she said.
However, she stressed that the major conversion works would take some time to complete.
"This is the beginning of a major journey," she said.
"It is going to take a year - I have to tell the public that we are going to have boards around the town hall.
"But my goodness me what a fantastic facility it is going to be for the area."
Work is to officially begin to create an art gallery in Kirkcudbright which could host one of Scotland's most significant hoards of Viking treasure.