Analysis of sediments in a Ghanaian lake shows the last of these "megadroughts" ended 250 years ago.
Writing in the journal Science, the researchers suggest man-made climate change may make the situation worse.
But, they say, the droughts are going to happen again anyway, and societies should begin planning for them.
"It's disconcerting - it suggests we're vulnerable to a longer-lasting drought than we've seen in our lifetime," said Tim Shanahan from the University of Texas in Austin, who led the research team."What West Africa won't handle - and neither will California - is the 100-year-long, deep megadrought"
Professor Michael Schlesinger