The first ukuleles were made in Hawaii. They weren't really invented so much as evolved from guitar like instruments. They were made by Portuguese immigrants as early as 1879. They were based on a similar instrument, the machete, that is found in Portugal.
Three Madeiran (Portuguese) immigrants immigrants, cabinet makers Manuel Nunes, José do Espírito Santo, and Augusto Dias are believed to be the first ukulele makers.