The scheme will see the town hall converted to house "nationally significant" collections.
Kirkcudbright Common Good Fund agreed to support the project with a total of £130,000.
The money will allow the creation of a second floor gallery to host a hoard of Viking treasure found in the region.
An additional slice of funding has been agreed in order to allow £3.1m plans for a major art gallery in Kirkcudbright to proceed.