1712, "belonging to a prehistoric age," see old + world. Meaning "of or pertaining to Eurasia and Africa," as opposed to the Americas, is by 1877. The noun phrase Old World in this sense is by 1590s. The division of the earth into Old World and New World among Europeans dates to 1503 and Italian explorer Amerigo Vespucci's use of Latin Mundus Novus for the lands of the western hemisphere found by Columbus and others, indicating they were not part of Asia.
The Known World is usually divided into four Parts, Europe, Asia, Africk and America. But it is a most unequal Division, and I think it more rational to divide it thus. Viz. the Known World, first into two Parts, the Old and the New World; then the Old World into three, Europe, Asia, and Africa; and the New into two, the Northern and Southern America. [Guy Miege, "A New Cosmography, or Survey of the Whole World," London, 1682]