The Hawaiian ukulele is descended from a Portuguese instrument brought from Madeira in 1879 along with the cowboys who came to work the cattle ranches on the Big Island. Traditionally it's said to derive from the four-string braguinha. However, I just discovered an interesting discussion on this site about how it may have originated as a direct modification of the five-string rajao. Never having seen either Portuguese instrument I can't be sure, but the rajao theory sounds good. The author of the article says that when he showed his ukulele to people in Madeira, they all said it appeared to be a modified rajao, and the tuning was similar.

Aloha,
Mark