Development director Peter Guthrie says, "Hugh Grant donated a lot of money. It was a very generous donation which we are most thankful for.
"We've been lucky - all our funding applications have been successful. It's a good project and people are getting behind it."
The actor's father Captain James Murray Grant served in the Seaforth Highlanders, while his grandfather was a commander at Fort George after World War II.
Museum bosses have raised more than $4 million so far.
Restoration work, which will include the building of a heritage center, is expected to take two years when it begins next summer (12).