Archaeologists have long been puzzled by the appearance in Europe ∼40-35 thousand years (kyr) ago of a rich corpus of sophisticated artworks, including parietal art (that is, paintings, drawings and engravings on immobile rock surfaces) and portable art (for example, carved figurines), and the absence or scarcity of equivalent, well-dated evidence elsewhere, especially along early human migration routes in South Asia and the Far East, including Wallacea and Australia, where modern humans (Homo sapiens) were established by 50 kyr ago. Here, using uranium-series dating of coralloid speleothems directly associated with 12 human hand stencils and two figurative animal depictions from seven cave sites in the Maros karsts of Sulawesi, we show that rock art traditions on this Indonesian island are at least compatible in age with the oldest European art. The earliest dated image from Maros, with a minimum age of 39.9 kyr, is now the oldest known hand stencil in the world. In addition, a painting of a babirusa ('pig-deer') made at least 35.4 kyr ago is among the earliest dated figurative depictions worldwide, if not the earliest one. Among the implications, it can now be demonstrated that humans were producing rock art by ∼40 kyr ago at opposite ends of the Pleistocene Eurasian world.