According to Produce Pete,"This variety is a cross of Red Delicious and Ralls Janet bred at a Japanese research station." It was introduced to the American market in the early 1980's.
I will permit myself a brief digression on the level of discourse you can expect when reading up on Apples. Almost all of the online resources I found for apples, were thinly veiled opportunities to plug the growing conditions unique to Washington state or the grit and pluck of Washington Apple farmers. Phrases like,"Washington State is the birthplace of the world's best apples" are thrown around without the slightest qualification.
I had my first Fuji apple relatively recently. I picked one up at Berkeley Bowl a few years ago and fell hard for the consistency. I've heard people describe Fujis as "super sweet", though I think what they are noticing is actually the lack of a prominent tart or tangy element. I've also not been able to find a good description of the taste that I think of as unique to these apples; definitely clean, but almost savory as well.
While the Fuji is a late-season apple, in the Bay Area you can find them pretty much year round. I picked these up at the Grand Lake Farmers' Market, from the stand where I got my Pink Lady and Crimson Gold apples.