The correlation is remarkably strong, and becomes even more apparent when you take a look at some of the maps here, particularly the map that shows the population density of African-Americans about halfway down the page. You can also see tinges of the same pattern on maps showing results by county for all the presidential elections going back to 1860 (!) -- the pattern doesn't hold that far back, of course, but you can see it to varying degrees in every election since 1968 (although Jimmy Carter's being from Georgia dulls the effect somewhat in 1976 and, to a lesser degree, in 1980.
If you want to take the effect back even further, here are maps showing how ancient geological forces laid rich soil in certain areas of the South, thereby creating prime cotton-growing areas and, eventually, counties that went heavily for Barack Obama in2008.
On a related note, here's a complete national map of the African-American population density, which I also found really striking. I hadn't realized just how much of the US black population was concentrated in the South. Look at the West, and how empty it looks, even in the more urban areas. There are maps for other ethnic groups, too. Now that would make for all kinds of interesting overlays.